What would you change in Heroes of Might and Magic IV?

I assure you, Equilibris made the game resemble Heroes 3, because in that game, if you don't have a free slot for creatures, whether through diplomacy, charm, or necromancy, you'll have to part with some of your own. Otherwise, the recruited creatures will disappear. And in the actual game, this problem of choice rarely occurs.

Yes, I remember how it was in Equilibris – you don't need to remind me :)
Frankly, I don't see the point in introducing this feature. You still won't be able to recruit a large number of creatures of another race, whether through charm or diplomacy. And with creatures of your own race, everything is simple and clear without any fixes. Apparently, in Equilibris, they removed the ability to add creatures as an additional army, considering it an imbalance. Well, on an XL map, this can still be considered an imbalance (you can actually hire five auxiliary armies from neutrals), but when playing on a small map, the skill of recruiting foreign creatures is completely meaningless anyway.
The problem is that in Heroes 3, there were UPGRADES. A nasty, annoying, and useless feature that didn't add anything beneficial to the game. Because of these upgrades, there were a lot of problems: Necromancers couldn't turn skeletons into skeleton warriors (because the "Necromancy" skill only created regular skeletons, which, without a special slot in the army, simply disappeared). For example, you come across a group of 500 Gnolls. And you have to think – either discard your 400 Gnoll Marauders for them (and then pay money to upgrade these five hundred to Marauders), or miss out on such a great opportunity to replenish your army.
And in Heroes 4, the only thing that can be annoying (if Equilibris is installed) is that you won't be able to recruit Djinns, for example, if you already have Nagas in your army. But it's not too upsetting, since you can't gather many alternative creatures, and you won't take them to the endgame anyway.
Regarding capturing a mine with an army without a hero – I have no ideas. As a random thought, I can only suggest this: a hero-less army marches to the nearest tavern and hires a hero. Or it finds a tomb on the map, goes to the Sanctuary, and revives a hero.