It is indeed more mechanical, in the sense that there is no ambiguity in the calculation. The rule is exact. Its execution can be driven by a machine, free of human supervision. A computer can execute the recursive function for exponentiation autonomously, and thereby mechanically calculate any exponent. By this technique recursion has acquired self-motive power.
Computers execute recursive functions every day.
This limit, should it exist, would be relevant to the critique. Any computational limit on recursive functions would set a corresponding limit on the powers of recursion in corporeal bodies, including the human body. Some mathematical proofs speak to this point. Hence its value can be computed in a finite amount of time. Partial recursive functions have been proved equivalent to those functions computable on abstract Turing machines.