Hrm? Suppose you're trying to accomplish some problem X. There are range of algorithms and heuristics available to you. You try a few of them. At some point -- usually a very quick point -- one of them is good enough for your practical purpose, and you stop.

We don't typically go too far in formalizing our purposes, generally. But I don't see what the deep point is that you're driving at. For practical purposes, algorithms are chosen by people in order to solve practical problems. Usually there are a few layers of formalized intermediaries -- compilers and libraries and suchlike. But not very far down the regress, there's a human. And humans settle for good enough. And they don't have a formal model of how they do so.

There isn't an infinite algorithmic regress. The particular process humans use to choose algorithms is unquestionably not a clean formal algorithm. Nobody ever said it was. The regress stops when you come to a human, who was never designed and isn't an algorithm-choosing algorithm. But that doesn't shed any light on whether a formal algorithm exists that could act similarly to a human, or whether there is an algorithm-choice procedure that's as good or better than a human.