As far as I've seen, there's no problem with minions and idols, aside from the bug with 2+ of the same type, ofc. I've been playing QoT most of the games, and the minions get countered pretty easily. Newer players (as in, first game or so) seem to have problems with them, but mostly players can just ignore the minions and go after the DG. It's harder, with the minions blocking and doing damage, but doable. It feels pretty balanced, as at least with QoT minion build I can barely kill DGs. I can assist teammates, push the creeps and destroy towers, but I can't chase or burst DGs. Which, among other things means, I don't get that much gold, and buying/upgrading idols is often away from survivability, mana regen and damage. Mana isn't that big problem normally, but resummoning minions is a strain till late game.
Should minions give exp/gold when killed, I'd pretty much go for other builds. Killing minions isn't that hard for many DGs, and when there's incentive for doing so, minions would end up dying all the time, while fattening up the opposing team. One fix might be adjusting the cooldowns, 25s is pretty low. On the other hand, if the minion army has just been killed, the DG is pretty much useless until it can summon more. Could be good thing, though :/
Also, on late game, when mana isn't that big issue for summons, assassins and minionless generals tend to get pretty strong. Using minions should also scale all the way till late game, and not become obsolete at some point, when the DG controlling them can just be killed and the minions ignored.
Some kind of aura solution sound nice, I don't see any big problems there.
Ofc these are just my feelings about this, and it could be that I'm simply not very good at the game, or at using minions. But it's pretty early to say much about the balance anyway, as so many people are new to the game.
And Marikir, summonable minions didn't exacltly lead to last hitting in DotA, it's present all the time. And it's micro hell, especially on melee heroes. Generally, summonables in DotA aren't worth killing if it's just possible to go for the hero, as they aren't that dangerous, but if one wanders conveniently near, free gold. Except Necrobook summons, summons in DotA don't really need that much micro. Pretty much because of control groups, and summons not having their own minds 