> For all practical and theoretical purposes, what matters is that the machine being considered does not exhaust its ability to recurse while performing the computations being considered.

You're right, and thanks for the more strict definition.

Regardless, the 'recursion limit' of the human brain is really low. (Say, seven things at once or thereabout; not going to links proofs but it's a non-controversial statement.)

Certainly not enough to implement any sort of computing machine. Human brains are notoriously bad at arithmetic and state machines.