Items balance is a bit .... whack

Staves on troops are, actually, very effective. Mostly because they ignore armor. And one can scale them with trinkets.

And what is wrong with power progression? With linear one we will end up with never ending battles, where weapons are not dealing damage to armored troops. Also don't forget that player should receive remarkable reward for reaserching technology, and 16 -> 18 just do not get there. 

+5 fire is huge. One should work hard to achive that. Enchanced axe + trinket + enchanted fortress. Or go staves and spend lots of crystal.

For the heroes weapons I agree with your points. The most rediculous part is mages preferring swords above staves.

Redicolous point scaling is exactly what causes such things to begin with.

with normalized values, that is less likely (and early troops remain move competitive, late-game troops are slightly less awesome)

Oh, lets not forget that mage troops really have no viable weapon upgrades for 99% of the game.

Perhaps you might want to do a little bit of math, first off. The game computes weapon damage as follows:

damage_dealt = rand(0.5, 1)*maximum_damage

maximum_damage = (1 - damage_resist)*Attacker_attack*Attacker_attack / (Defender_defense*(1 - Attacker_penetration) + Attacker_attack)

Most units have no resistance to physical damage, so for nonmagical weapons that term is usually 1. The main exceptions to this rule are Banshees and female Undead race units. No unit has a nonzero defense value for an elemental damage type, so elemental damage reduces to the attack score multiplied by the resistance. The end result of this is that the theoretical maximum damage of a purely physical attack against a target whose defense score is equal to the attacker's attack score is only half the attacker's attack score. In other words, end-game weapons against mid-game armor are unable to deal more than about 10 damage per figure. When you realize that the only targets that your staff units lose damage against are those with an appropriate elemental resistance and therefore can deal up to 6 damage per figure against most units (which reduces to up to 4.5 damage per figure against units with one of the 25% resistance cloaks, or up to 3 damage per figure against units equipped with one of the 50% resistance cloaks, if the cloak on that particular unit resists the correct element, and increases to up to 9 damage for ice staves against Quendar who aren't equipped with the +50% cold resistance cloak), the staves don't really look that bad (these figures do not include sources of additional elemental damage, though those stack with staves), especially when you consider that they're a ranged weapon available on an extremely early tech and yet are still capable of dealing damage against mid-game armor similar to the damage that end-game melee weapons would deal against the same target. Note also that the additional elemental damage you can add to units via trinkets and spells reduces the single-hit damage disparty between staves and mundane melee weapons, as it more or less adds a fixed amount of damage to both units.

Actually, I'd say that mages prefer daggers, as daggers have a greater initiative bonus than swords do and typically also carry critical hit chance or critical damage bonuses, both of which affect damage spells, then staves which have the spell damage/cost/mastery bonuses, then swords, then anything without an initiative penalty. Daggers and staves with spellcasting bonuses can change places depending on what the exact bonuses offered by the weapons under consideration are and what kinds of spells the mage casts, and the same is true of swords and staves with spellcasting bonuses. The fire and ice staves and their upgrades are worthless on champions, but that's true of the majority of regular unit weapons anyways.

Can you elaborate, please? I can't catch how high attack lead to not dealing damage?

If you look to others games around (4X and not 4X), you'll see that characteristics scale with exponential pace for a reason. I highlighted that a bit in the first post.