In practice, people write their programs in a programming language. Some languages (e.g., C, Java, Lisp) only provide leaky abstractions, so programmers always have access to the internal representation of everything, to the detriment of modularity. But there are languages (e.g., Standard ML) that aren't hobbled in this way.
> Those all speak to the issue of how difficult it is (for e.g. a human) to implement the function, not whether language/computation model can compute it at all.
No. In Standard ML, writing a function that inspects the representation of an abstract type isn't “difficult” - it's literally impossible. If you want to do it, you have to use a different language. The type system enforces the separation of concerns, so that you don't have to rely on your discipline alone.
> If you have a computation for which no TM (or asm, C, etc program) exists that computes it, let us know!
Re-read my sentence. I was talking about the converse: There exist programming languages that don't allow you to do everything the target machine can do.