Some ideas:

A tree that gives extra spell books for more spells.

Ability to convert normal weapons into magical ones

Genocide- be able to wipe one type of monster off the face of the earth entirely.  This should cost mana based on strength of monster

Quick cast- be able to do a spell , unit still gets to take its turn

Polymorph- transform one of yours or one of the enemy's unit into something random

Could someone post the existing Wizard tree so we have a visual reference to help improve it?  

Love the idea that he does not take a unit's action to intervene/cast spell.

I envision myself less of a leader and more of a researcher and spellcaster. 

There could be a trait to improve the chance of my hypnotism working.

I love this idea, +10% or even +20% faction-wide for those damage types would be neat. Could also work in reverse, giving your entire faction +10 elemental resistance to a particular damage type. 

I would also like to see some kind of unique city enchantment, something related to mana but not a straight up buff to mana production. Like... Elemental Affinity - units produced in this city gain +25 to one of the elemental resistances.

Another cool thing would be to have some kind of ability unlock for battlemages after the improvement to build them is unlocked.

It's a bit odd to have all that mana and Tandis the Uber-Slasher as your hero   with +mana-per-kill enchantments   They dovetail with synergy: we'll (ab)use multiple sov casts to carpet-bomb or pin-strike whatever Tandis can't already solo.

There's still the broader problem (discussed briefly in a stream) that many tactical spells are just coaster/screensaver uninteresting, and you'd never waste a sov cast on them, even if you had 5.  So any change toward large mana reserves + many sov casts stumbles over this rut etched in the streambed: we'll all just beeline for k of the biggest area-effect damage spells we can research.

• 3 Blizzard in your first 3 actions is probably more efficacious than 3 of anything else.  Or ...
• 3 Flame Dart might suffice to take out any trog archer or evil spellcaster group.  Remaining fodder are Tand-able.

I'd love a Wizard tree that enables many sov casts (including getting all that mana), but rewards creative thinking ... or enforces it.

• Non-repetition.  One really silly/fun/wacky way to make the wizard truly be a caster of many spells is to enforce "non-repetition" of sov casts.  Let "non-repeated spell" be a spell you have not used "recently", at least in your last 1-2 combats, including this one (but we can define other durations, e.g. using turns or per-group).
• Battle history cooldown.  You get k sov casts, but they may not repeat.
• Research bonus version.  Every time you sov-cast a non-repeated spell, you gain +q lore.  So you get more spells faster, yaay!
• Research penalty version.  Or, every time you repeat, you lose -q lore.
• Sov cast version.  You may cast any number of spells without reducing your sov-cast counter, as long as they are non-repeating.  (i.e. once each, through every tactical spell you know )  Your first repetition counts as a real sov cast.  No quintuple-Blizzard for you!

Another kooky idea (which is almost possible already) is to make spell combos feasible and worthwhile.  This is simply a sequence of 2+ spells that stack on a target for total effect far beyond any 1 spell alone.

• Any summon + the Blaze of Glory-ish.  Summon a temporary dude, e.g. wisp or drake.  Buff him with the "you die at end of combat" spell.  He was "dying" at end of combat regardless   For two sov casts that aren't two Blizzards, you deserve to have one guy who'll do more than two Blizzards' worth of total damage.
• Reduce spell resistance + Blizzard.  Haha.  It's still more interesting than two Blizzards!
• Limpet + pinbomb.  Target your own guy (e.g. Sir Kael).  Now he's a Marked Man, and his normal attack changes to ... grapple with his opponent somehow.  Instead of dealing his normal combat damage, he immobilizes his melee target, or cuts its resistances, or otherwise sets it up with a weakness.  Then you sov-cast something else through that weakness.
• Mesmerism.  Or, it increases your sov ability's % rate, so you can Hypnotize something that would normally resist.

This suggests a skill in the Wizard's Diplomacy branch:

• Craft Ring of Sov Cast.  (Celebrimbor) Permanently reduces your sov cast by -1.  This ring may be equipped only by a Minor Race Hero.  In combat, that hero's group gains +1 sov cast.  You may gift this ring to an unallied minor race, which grants +k favor instantly.  (Tweak: There exist some really persnickety minor races that cannot be allied in any other way.)  If bearer of this ring dies, ring drops as Loot For Monsters, which persists on the map, and can be picked up and wielded by monster groups.  If you beat that monster group (and it will Blizzard you), you keep this ring as loot, until ...
• Uncraft Ring of Sov Cast.  Very high in the skill tree

I like the cited suggestions. 

Although I would maybe change "Instantly Learning High Level Spells" to provide a recipe for instant-learning a high level spell. The recipe could tailored to a specific category of spells e.g. wrath, enhant, chaos etc. The recipe would require expensive ingredients ex. 1 radiant diamonds, 1 radiant topaz, 1 radiant emerald and 1 radiant ruby along with 50 mana. By providing recipes with expensive cost you give the player the option of choosing the specific spell or spell category from which to instant learn spells. Further with the high costs it also ensures that this is not misused. 

I really like Unlimited Research Options, as I think it is natural for the Galor to choose more wisely as it is assumed Galor has superior Arcane knowlegde compared to these wanna-be wizards, who think they are One-Wizard to rule them all.... tsch, imbecile priestcommandertyrantlittlemantinker. 

More Starting Mana is a natural / must for the wizard. He is the wizard and thus has focused more on arcane magic. Hence he should have built a bigger hoard of magic than any of these imbeciles wannabe wizards.

More starting spells: As a wizard you have more arcane knowledge - hence you must also have access to more starting spells. This can be balanced with weaker starting units (leaving Tanis aside). For example give him 'heal', 'haste', 'blind' or some of the other common spells. This could be 1-2 in addition to Fire Dart and Harvest spells.

Heal shards: I think as a wizard using shard-power, and shards being in the realm of arcance power, the wizard should be able to heal shards or at least do something with them. I think heal shards is also present in Priest, but I see the Priest being more about divine power/punishment. No so much about shard healing even though the Gods could heal them. Maybe move heal shards for the priest to a divine favor.

Spell of Domination: I think the wizard should have the option of casting a Spell of Winning, the same way as the tyrant, where the wizard must acquire all or a large part of the shards (depending on the map type) and win the game. 

Background: Galor had an ambition of becoming the equal of Eregog. Hence he pursued arcane knowledge. He knew that Ceresa and Mithar also pursued the same goals. Fortunately he was able to defeat Ceresa, but unfortunately he did not pay much attention to Mithar. While Galor defeated Ceresa, Mithar took advantage of the chaos after the war and rose to power. After it was too late, Galor realised his error in losing track of his competitor (Mithar) and could only watch while Mithar defeated and destroyed most of the known world. Galor himself only survived through pity from the Mithar, and Galor lost most of his power. He know bide his time waiting to strike back with his revived arcane power.  He becksn and crawls while he sits in his tower lab, researching old arcane magic from ancient times. He might have unearthed a tome of Eregog or maybe it is Moridan from which he develops his arcance power in order to be able to cast the ultimate spell, Spell of Domination. Spell of Domination will make the other imbecile wannabe-wizards beck to his call and whims, making him the Master of the universe world. Ha ha ha - Mithar you just wait - I will come for you.... Now bow before me, Ha ha ha ha ha........ 

I AM the Master of the Universe - HeMan.... dudu dum dum duuu duuu dum dum....

Galor we love you!

Grand Scholar: +1 to all spellbooks the wizard has at least 1 in.

Magic Siphon: Wizard gets +1 mana from any spell cast by the opponent

+to the idea of giving Galor more spells only he gets!

Galor actually makes more mana from shards and his spells costs less mana, and those skills are at the root of the skill tree.

He is ok, except for clairvoyance thing, which doesn't play well as a core mechanic.

Well, using Gandalf as the exemplar, he actually didn't just go around spamming spells.  His excuse (quite deep, befitting Tolkien's craft) was that the enemy (Sauron + corrupted palantir) was both far stronger and had farseeing, so that any major use of his magic would allow Sauron to pin-target nukes.  More deeply, Gandalf was no match for Sauron 1-v-1 at any time, and certainly no match for Sauron's 3,000-year-old war machine infrastructure.  Nonetheless, Gandalf (Olorin in the West) was tasked with one mission: "Take Sauron down".  How do you do that when the enemy is basically the Emperor and you're only Admiral Ackbar?  Maybe you rally enough nations to actually field 20 divisions to match his 30 divisions.  Hence Gandalf did exactly this, and it kinda-sorta worked.  No other strategy would have!

In fact, in the entire LotR trilogy, Gandalf makes blatant use of his powers exactly thrice:

1. During the Fellowship's walk toward Rivendell, Gandalf briefly leaves them, and gets ambushed by the Nine on Weathertop Hill.  Since they're already in his face and they have sat phones with speed-dial, secrecy is no longer the concern, and he lights up the nighttime horizon with his lightning, so that the Fellowship gazes at it in wonder from several miles away.  Yah, that was Gandalf Unleashed.
2. At the top of Moria, Gandalf duels the Durin's Bane balrog, and blows it away.  And then dies from the effort.  In March Madness terms, it was maybe the 8-9 match-up, with Sauron as the #1 seed ...
3. During the siege of Minas Tirith, Gandalf rides out to rescue the comatose Faramir, and lightning-bolts a Nazgul that flew too close.  He's got yer AA point-defense vs. fighters right here ...
4. Outside Moria, when the Fellowship was close to freezing to death, he basically lit a torch, and complained that even that little magic was too much to escape Sauron's notice.  Deep in Mordor, Sauron instantly received a FLASH THUNDERBOLT tweet saying: "GANDALF IS HERE", with a little pin in the map showing location and elevation, and nodded, then scrolled his mouse to follow the Fellowship around within that vicinity ...

Other than that, Gandalf mostly uses his voice, and sporadically swings Glamdring.  Recall how he tricked the three dumb trolls in Hobbit.  He's been the Passive Observer on a Hill in at least three major battles: Battle of Five Armies (Hobbit), Pelennor Fields (Two Towers), and Minas Morgul (RotK), and didn't cast a thing in any of them.  In fact, all he did was use his voice: "You shall not pass!" once and "the Eagles are coming!" twice.

So ... for a spell-spamming mageslinger, we probably need to look for other role models.  Remember that Tolkien wrote LotR during the grim years of WW2, when Allied victory was not at all assured, and so he couldn't just resort to the childish wave-my-hand-and-just-win-now solution.