The point is that creating hardware that executes a Turing machine or something like it is easy, but constructing hardware that executes a general recursive function is so hard that it has never been done.
My point was that a random mathematical expression will not be constructive in itself. And you are right, that either general recursive functions or lambda expressions are required to be equivalent to Turing machines. And while I agree that recursive functions are hard to execute on hardware - but certain aspects of it are apparent in CPU design — out-of-order execution is sort of lambda-like.
The point is that creating hardware that executes a Turing machine or something like it is easy, but constructing hardware that executes a general recursive function is so hard that it has never been done.