I kind of love it! I think what could work as a good compromise, if the wizarding world was unwilling to part with the house system as it was, is having that extra Sorting at the end, in private, just so graduating students could think over their own personalities and the housing system, and gain a better understanding of themselves and others.
Random thought - perhaps pupils could be sorted when they leave school instead. So you would have four randomly assigned houses throughout school, and then when you leave you get the big once-a-lifetime sorting. It could even be done in private, and it would turn it into quite a nice, personal, reflective experience for people about to enter the adult world for the first time.