Yes, that's a good point, and in our interviews we do try to take a slightly less well-known problem, at least one that doesn't have a dozen well-known named algorithms.
Still, even using a pre-learned algorithm demonstrates some level of confort with algorithms in general, and can be used as a stepping stone during the interview to shift the problem slightly to see how they adapt the algorithm.
For example, if a candidate is clearly taking their time and essentially working out the algorithm themselves, and succeeding, that demonstrates the skill and we can move to other problems. If the candidate just breezes through and finishes in 2 minutes, then we can change the problem ad-hoc to try to get them off the beaten track a bit (say, if they wrote quicksort, maybe ask about making it stable, or sorting even numbers differently from odd numbers, off the top of my head).