While it sounds like a cool concept, I worry how it would effect unit identity/individuality. I agree FE restricts classes arbitrarily, which is stupid. Letting players really build whatever units they want is a great way to let players craft their own experience. This would also increase replayability of the game. The different types of armor, mount and weapon combinations could also lead to some fun challenge run ideas.
On the flipside, if anyone can be anything, it will make each unit feel less distinct (a problem I had with Three Houses and late game Echoes). Balancing would also be tricky, since the developers can`t know exactly what units players will bring to later chapters.
This premise, while far from rare in modern stories, does offer some interesting opportunities. Letting the player switch factions midway through could offer some intense confrontations later in the game.
I could see a potential problem if the factions were not created equal (like what happened with Fates), but that is just a possibility.
As for it being better or worse than what FE currently has, that depends on execution. A simple premise executed well tends to be better received than a unique premise handled horribly.