Why? You're testing their ability to produce the right answer to a given problem - not their problem solving ability. To that end it shouldn't matter if they've seen the problem or not.
I always find it hilarious when recruiters say that "getting the optimal solution isn't everything." I've failed numerous interview rounds where due to time constraints or implementation details I'm not able to completely code the optimal solution, but I am able to talk/walk through each step of it in pseudocode with the interviewer. By your own criteria, being able to clearly explain the solution and demonstrate an understanding of the different tradeoffs should count for much more than just being able to copy/paste the solution from memory, but I've never advanced in any round that finished without a "working" piece of code.
Honestly, the one thing I appreciated about FB/Meta's recruiters is that they were always honest about the process and what was expected - 2-3 Leetcode mediums/hards in 45 minutes and they only care about optimal solutions. I much prefer that to disingenuous sentiments of "getting the right answer is important, but we also want to see your thought process and how you might work with another engineer on the team."