Conceptually, that's a good approach -- indeed, we've used that at times in the past. It's one motivation for the Emerald City Productions style of questionnaire, which is more quantitative than most.

But in practice, my questionnaires produce so much data that there is no such thing as a perfect fit, and even getting a good fit for a single player can be tricky. My guess is that it would have to be done with numerical approximations, and that's subject to various pathologies. Balancing the importance of the various questions is utterly crucial and quite difficult, and my suspicion is that most algorithms will be subject to getting stuck in local minima. So I can imagine a program that would *help* with the process -- essentially a spreadsheet for casting, that allows you to tweak and tune and see what happens when you change things. But it's difficult at best to do it well in a completely automated fashion.

Indeed, I think it's probably a bad idea anyway, because you learn a lot as you cast. I hit frequent cases of, "Oh, that player won't enjoy that character because of X", which usually indicates that X is actually a bug in the character, that needs to be fixed. Games change and mutate a *lot* as you attach faces to the characters. (At least, mine do: I pretty much always wind up customizing the game somewhat, and it's always for the better.)