Types give you the power of abstraction -- they allow you to define new concepts that "don't to go wrong" and allow you to speak of things other than just bytes-shuttled-on-a-turing-tape. Rigorously justifying the ignorance of the underlying bytes (i.e. being parametric over representation) is an advantage, not a downside.

But maybe I am misunderstanding your comment? Perhaps you were just equivocating over what "really there" means? If that's the case, is multiplication not "really there" because it can be implemented in terms of bit shifting and addition? We don't imagine multiplication as somehow putting these restrictions on what we can do with our bit shift operators -- the multiplication is the "real" thing we care about and the binary operations are incidental.

In any case, see the famous parable that opens Reynolds' "Types, Abstraction, and Parametric Polymorphism" for a colourful example of ignoring the underlying data representation:

http://www.cse.chalmers.se/edu/year/2010/course/DAT140_Types...