Guaranteed permadeath as you describe wouldn't do anything to make champions balanced. IMHO, "balance" comes down to the fact that the AI currently doesn't use their heroes as well as good human players would (for example, I have never had an AI champion cast a direct-damage spell).
Champions are balanced against each other, but the AI just can't keep up with a competent player. So by the time the player is ready to go to war, his champion is 5-10 levels beyond where the AI's champs are and twinked to the sky from loot drops. If your hero had parity with the AI's and faced off alone against the AI hero with backup, he'd be back home nursing his new wound before you knew what hit you.
Currently, players are able to plow through the game with their uber-champ without dying ever. Really this would just handicap players who are already struggling to master the game. Your suggestion would make no difference for good players and make the game much harder for novices.
Increasing the likelihood of permadeath (if it's still in the game, I haven't seen or heard of champs dying in any game I've played) on higher difficulties might be something worth looking into, if it did add some extra tension to the game.
And I like the idea of applying a permanent change to the spot where the champion dies. Maybe it could have an effect depending on the type of hero? Like some make it settleable, another might spawn a monster lair nearby, or a quest, or a goodie hut.
I also like the idea of being able to hire champions away from your opponents (or have them hired away).
There could be a mechanism to would spawn new champions/quests/monsters randomly as the game progressed. That way, if your heroes were dying or being stolen, you'd have a chance of recovering from that. The opposite problem, however, then rears its head. You don't want one faction with dozens of champions, either.
So maybe you'd only spawn a new hero when an existing hero dies. How about introducing hero aging, with the more time they spend fighting the faster they age, up to some rng generated lifespan at which point they die. You could have potions of vitality and traits and wounds that affect the lifespan. Fun stuff (as long as you don't have to program it or train the AI to use it).