Solving a difficult chess puzzle is one thing, solving it fast is even more challenging. Does the speed of solving difficult puzzles increase with increasing elo in addition to acquiring the ability to find the best move in challenging situations?
Generally speaking, doing "Puzzle Rush" style training will help you see the board quicker and train your intuition "where the candidate moves might be" ... But I always say Accuracy first, then Speed.
Your question is a little confusing, are you asking if better players can solve harder problems quicker? Probably yeah.
Look how quickly GMs can do Puzzles :P
Speed comes with exercise. Skill comes from solving correctly the chess puzzles. Practicing the same errors hinders development.
Practicing the correct responses, increases speed. You don't want to continually blunder the same type of tactics.
So use the dashboard (lichess.org/training/dashboard/30/dashboard) and work on the lowest rated tactics that you are blundering on the most.
Maybe physical exercise is all that chess experts need to become masters. Does the VO2max effect memory? If so, than ...
Has anybody checked the VO2 max of a grand masters ?