The "internal, ambiguous type" matters when you try to actually invoke (show . read) on some String. If you want to actually use that function, you're stuck inserting a type annotation, which would lead many people to say that (show . read) is not "inferred just fine."
There is no internal ambiguous type. It is not a concrete type, it is a type variable. But it is inferred just fine. It is (Read a => a).
>which would lead many people to say that (show . read) is not "inferred just fine."
Even if you were to erroneously say that, it isn't type classes that is the problem.
I'm pretty sure it is. For example, see section 3.7 of "Type classes: an exploration of the design space" by SPJ et al.