you do need different implementations for different types, so "overloading by hand" is inevitable. It's nice to have compiler do it for you.
I agree that templates represent another, backdoor attempt at real type system, after virtual functions failed to deliver. I am beginning to think that templates are simply Smalltalk-style metadata, represented in many, many versions of generated code. Just like in Lisp one can implement lists with closures, the same way one can replace metadata with lots of generated code. To some extent. There have to be better statically-typed languages.