There are some such algorithms. You don't encounter them as often because we are biased towards encountering algorithms that can be implemented efficiently or at least can be approximated efficiently (i.e., a great many "NP-complete" problems admit of usable approximation algorithms with varying degrees of usability).

Plus, in perhaps a bit deeper philosophical sense, we are ourselves biased towards expressing problems that have relatively simple complexities as their solution. While there are some simple problem that have complicated optimal solutions, certainly, I'd say that in general the vast bulk of problems for which the optimal solution has Ackermann's complexity are problems that we can't really express or manipulate, either. We focus a lot on our ability to create and express solutions because problems in the real world tend to force themselves upon us since long since before computer science was even a thing, but our ability to express problems is limited too!