I disagree, to some extent at least. The sorting hat decides which person would have wanted you in their house the most. Choice becomes a factor only because the founders wouldn't want someone in there house who didn't want to be in it.
I don't think there is some complex unlying what ever, I seriously doubt JKR would have taken the time think it all up.
You guys remind me of these cult guys who became enthralled with a direct to video release last year that had lots of plot holes. They fanbase that became enthralled with it and tried to reason out reasons why certain things were happening, they came up with lots of perfectly good reasons, but, what it turn out was it was put together by a first time director who wasted all his time shooting and had to edit the movie in 15 minutes, and that it truelyy had only peiuce of a plot there was never any reasoning behind what happened, they didn't have time to make up reasons for everything, just as JKR doesn't have time to make up reasons for every last element of her book, she just puts things out there. That's what make the story so real, you don't really know. Nothing is even implied.
But the sorting does say that it determines what founder would have wanted to teach you the most, and that is eactly what I think it does, no more, and no less. There is no reason why it would be more complicated than that, not one. At lerast not one you have pointed out.