> But do you want /width*width to be optimized?

I do. But I don't see such optimisation as anything to with your changing float type.

Changes like that will break just as much code as adding extra precision will. Because it will change how things round, and not much else, just like adding extra precision. They're both slightly disruptive, and they tend to disrupt the same kind of thing, unlike removing precision which is very disruptive all over.