A mosquito just bit me... maybe I was wrong. :( It's been a while since I played Heroes of Might and Magic III. :o But the ability to max out each unit definitely exists, and what else is needed for happiness...
By the way, I'll add the main drawback in HoMM3: imbalance, of course. The two weakest factions also get a limited magic guild... Horrible. If they are weak in magic, they should have been made incredibly strong physically. As it is... no one usually wants to play as them.