> The advantage of this approach would be allowing function overloading (similarly to C++ or Java) informally without interfaces or type classes.

I might be misunderstanding something, but how does this allow function overloading more than ordinary let-polymorphism? Functions can already have a type like, say, ∀a.a→Int. It's also quite common to do type inference in two steps where the first pass creates type variables and a list of constraints. The set of constraints are then passed to a unification algorithm, see e.g. http://www.seas.upenn.edu/~cis552/lectures/stub/FunTypes.htm....