It's the definition of Turning complete that's the problem. A Turning complete machine must be able to process countably infinite inputs. The halting problem arises from same thing. There is no halting problem if we restrict ourselves to programs that will stop in a bounded time (obviously).

In practice that means a true Turning machine can compute things that aren't actually computable in our Universe, or at least not by the bits of the Universe we understand well. I doubt any engineer will think that "this architecture can't in theory compute things not computable in this Universe" is a strong argument against it.