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).
Trivia does not provide evidence of skill, it demonstrates prior knowledge.
It would be better to introduce a unique situation that would place everyone at the same starting point.
Even so, knowing very widely talked about programming trivia is still a signal for interest in the art. I'm not sure that sorting algorithms are a good example of what I'm thinking, but I always award extra mental points to candidates who seem knowledgeable about the field (e.g. they know the general consensus on manual memory management vs garbage collection). Still, I wouldn't consider these sorts of things dealbreakers by any stretch of the imagination.
As a programmer, your task is to find algorithms to solve problems. Sure, sorting numbers is a solved problem and in real life you should use a library. But you will not find a library for each problem you encounter, and sorting is a very simple problem to solve compared to anything you'll find in real life.