I think it's important to think about architectural and domain bounds on problems and check if the big-O-optimal algorithm ever comes out on top. I remember Bjarne Stroustrup did a lecture where he compared a reasonably-implemented big-O-optimal algorithm on linked lists to a less optimal algorithm using arrays, and he used his laptop to test at what data size the big-O-optimal algorithm started to beat the less optimal algorithm. What he found was that the less optimal algorithm beat the big-O-optimal algorithm for every dataset he could process on the laptop. In that case, architectural bounds meant that the big-O-optimal algorithm was strictly worse. That was an extreme case, but it shows the value of testing.

Domain bounds can be dangerous to rely on, but not always. For example, the number of U.S. states is unlikely to change significantly in the lifetime of your codebase.