The imbalance is at its deepest level. I actually made 1500 cavalry units. And I defeated Agrael at the end of the campaign. He didn't even have time to react!
Haven forever!!!!!!!!!!!!!!
I can beat the single-player campaign, but I don't feel like playing this product in multiplayer...

That's a lie. You just had the Grail!!! And Agrael's AI was nerfed, otherwise he wouldn't have waited for weeks. And on a random map, Haven won't be overpowered because its early units are weak, while fairies or furies will bring much more resources and other benefits at the beginning of the game, creating a huge leap in development for these two factions. Necropolis with its skeletons will also be more effective at the beginning. And Inferno can effectively block enemy archers and expose units vulnerable to gate spells. So, in terms of development, Haven and Magic are at the very bottom. And there's also the last ability of the heroes, and it's the worst for humans.

And the imbalance WAS IN ALL PARTS OF THE SERIES. Moreover, it was HUGE, and Heroes of Might and Magic 3 is no exception. You can list examples endlessly. Necropolis with 600 skeletons on the 2nd week, 12 vampires that, with practically any hero, destroy the maximum-level griffon stronghold and get 4 angels. Flux with 6 birds also on the 2nd week, with fairies that can destroy any slow, non-shooting army, in any quantity. Spells like Dimension Door and Teleportation with a developed spellbook, and much, much more...