Because if you need to branch based on type more than a few times in your function it can get pretty hard to read. Am I right that the basis of your complaint is that it's now harder to find all the members of (what you'd call in C++) the "overload set" for a particular function? If so I can see your point.
Yes, that's my point. And it doesn't really simplify the function itself, it just rearranges it, in the same way you can break up a complex painting into jigsaw pieces and say, "Look, each piece is simple!"
I think the answer to the question "should I apply X refactoring technique to this function Y?" obviously has to depend on both X and Y. There's clearly a trade-off here. If I have a free function foo(x) that I want to work differently depending if x is type A or type B, splitting that means breaking up foo, sure, but because I can only ever call foo with an x of type A or type B (unless I'm converting some As to Bs halfway through foo or something awful like that) it might be useful to see all of the "A" logic in one place and all of the "B" logic in another place.
