One of the criteria for featured quizzes is that they shouldn't be too esoteric, and the average quiz taker should be able to take it and do at least somewhat well, but do you think this is limiting? I'm not saying at all that you should make quizzes only with the intention that they will get featured, but that is one of the aspirations for many quiz makers, including me. Obviously Quizmaster has the right to do whatever he wants since it's his site.
Anyways, just an idea that I've been thinking about, and I could be wrong about it, but I just wanted to give my take.
Realistically? Never.
For one, there are new things being made all the time (TV shows, people becoming famous, new fields of science) so there will always be new things to make quizzes on.
Secondly, there is always more and better data coming out which will help with new topics to make quizzes on that weren't possible before because there was no data.
Plus, people are so freaking creative. There are literally endless possibilities of things to think about and to quiz each other on.
TL;DR: Always increasingly more new things to create quizzes on, people are too creative to run out of ideas.