It would be really cool to have events and adventures or things in game that a hero can accomplish to gain a new form or special promotions. Great ideas!
Keep in mind that equipment is a reward for accomplishing a task that gives the successful unit (or empire) a boost. You can either look at it from the standpoint that the unit that kills Barbatos gets upgraded to a new form that gets death affinity, or that he gins an item that gives him death affinity.
We opted for the equipment version because it seemed more flavorful, its easier to implement, and it applies even to non-hero units. We also like that the equipment can be passed on to other units and can be taken/stolen back and forth between waring empires.
Form a game design prespective (ignoring flavor for a moment) the mechanics proprosed in this thread and the equipment system fill the same niche. The implmentation differences are that hero upgrades would:
1. Heroes would stay powerful throughout the game. Currently each hero is designed to be powerful only during a specific part of the game, saverous is a wrecking machine early on but by the time champions are around hes running out of steam. Heroes are powerful enough, we have no desire to boost them further. This change would also mean that early heroes would be inherently better than late heroes because they would dominate during their era and still be on equal footing with the late game heroes.
2. Your empire would be devastated if a hero died more than it is now. Since the game would be all about the heroes losing them would be hard to recover from. The nice thing about equipment is that even if the unit loses in combat a party can be sent off to recover the lost item (someday ill have to post my love for "active dynamic quests" over scripted ones).
3. Upgradeable heroes would steal a lot of the flavor of the grigori who have drab heroes compared to the others except for the fact that they are able to upgrade them (as cypher noted).
So in general I think its a bad idea, but thats just my 2 cents. I will say that we continue to expand equipment and 0.34 has at least 6 new pieces, 3 of which are won by defeating units. So when we think along these lines thats the way we usually implement.