Re: Would you play…
I've played in games similar to this, some more successful than others. The most successful was a one-shot where the game began with the pcs waking up with severe but temporary memory loss. In the course of the game we had to figure out who & what we were, and what was going on. It was great fun but I certainly wouldn't have wanted to play a long-term game.
The least-successful is closer to what the OP is suggesting. We designed normal humans and the GM gave us powers during the first few sessions. We had several of the problems mentioned in this thread. Despite having an excellent GM and players, it just didn't work well. For ex., I designed a character with a detailed background and personality that would encourage (I hoped) the GM to give me particular types of powers. Instead, I gained magic. The character knew absolutely nothing about magic so I was forced to make a choice - play the character effectively but "not in character", or stay "in character" and not be particularly useful. I chose the latter, shocking the GM. Other players likewise had issues with some of the abilities they gained.
I think a game like this can be interesting, allowing players to explore different themes and ideas than they might normally. But that works best in a ione-shot or short-term game. For a longer game, It can be very difficult to feel attached to a character that you don't like or aren't comfortable with - esp. in a point-system like Hero, where much of the appeal is in character design.