I, too, probably would not take well to a character that my GM just handed to me. But for the OP, I'm picturing a short list of awesome characters, complete with awesome artwork, that sort of speaks to everyone. Even the bard (Edward!) looks awesome, for some strange reason. Would you want to play that, if you could pick from your favorites?
Background, personality, motivation and abilities are all tied together in a character I player, and the character has to be someone I could play with an emotional connection with. That includes all those listed things - and I am very particular about how it comes together. It could also be that I have a particular avenue of myself I want to enhance in the characters personality.
So I double it would work.
To put things in perspective - 2 of my longest played systems are D&D 3.PF and HERO. Those games have about the right amount of character customization for me to feel comfortable to play, and expect to enjoy (although PF is a little limited for that). I can take weeks to make a character just exactly what I want them to be. Add to that the fact that our games run long - my last 2 HERO characters had been played for more than a decade by retirement, and my last PF character for 4 years. I couldn't get long term invested in a pre-built character (even if awesome) for that.
My primary purpose in roleplaying is immersion, to maybe even have moments that I forget I am playing and completely feel the exact thing a character feels. For that work, the character has to be an extension of me, and for that to be the case, I have to create the character.
I think, in the abstract, your idea would work... but it would never be a game I feel comfortable playing. I would no more connected to what was going on than playing Sorry or Chess. It would just be completely mechanical and not what I want out of roleplaying. Even playing such a character for weeks and months I would never develop that .. emotional bond (for lack of a better phrase). It would always feel like moving pieces around a board and not becoming the character.
When I play I always refer to my character as me "I attack the ork" "What do I see". In a character I didn't create it would be "he attacks the orc." So again, it could be a great game, but one I would never play, as the basic concept is almost antithical to what I want out of roleplaying.
(Disclaimer some of that comes off a little one true wayism - I am only applying these standards to myself, not how other people play).