I wonder why Slytherin House remained at Hogwarts after Salazar Slytherin left. It would seem that someone so passionate about his views on the worthiness of students might have left and started a competitive school – and surely the students/parents who agreed with him would have followed him.
Along the same lines, it seems weird that Hogwarts would keep a house dedicated to the students whom Slytherin specifically preferred . . . without Slytherin around to nurture them. It would seem more natural to me that they would have done away with Slytherin House altogether and sorted future students into the other three houses based on their non-Slytherin attributes – and those non-Slytherin attributes would have been nurtured, probably for the good of all!