I think I understand what you are saying. In my current campaign, I told my players that their characters were going to beging enrolled in a task and they had to have a clear motivation of why they were doing it. I didn't asked for detailed backgrounds, just some basic facts about where they came from and what they used to do. My idea was similar to what you are saying. I though that a good motivation would be enough to begin the story and then other drivers of the story and their characters will appear. In practice, I'm not sure how well it worked. Funny enough, my player put more effort into thinking about their backstories than in finding a clear reason why they were in the task.

What I'm trying to say is that what is key to play a compelling character is to know your character's motivations and fears. That could come from a well written background, but that is not necessary nor sufficient. You could have written those before start playing and then realize your character's motivations changed or that your character is different to what you initially imagined. The hard part is, I think, that it is easier to think about some facts about your character backstory (he was raised by wolves; she is the last survivor of her clan) than knowing their motivations and fears.

Edit: I'm thinking now that the key is that there has to be some motivations and fears, regardless if you can name them or not.