Like I said before, there's also the issue of perceptions. In the first place, if people see or treat anything as a closed shop then it tends to stay that way; in the second place, you'd be surprised how easy it can be to accidently create a closed shop whether you intended to or not. To take an artificial example, a pub quiz whose music round is exclusively 60s-80s is going to be off-putting to people who aren't interested in that period, and ought to broaden its question pool.
As to the point about the balance of history, etc. The problem is that there are *two* main sources of imbalance in representation, and only one of them is history itself; the other is who we choose to focus on, and that choice tends to (wildly) exaggerate the biases that are already there. The key is to ensure that you've eliminated the second as far as possible -- no, you cannot escape the first kind of bias, but you can't hide behind that either to pretend that the second kind doesn't exist. If a quizmaster chooses to ask questions mainly about Einstein, Newton, and Galileo, but forgets to ask about Marie Curie, Ada Lovelace, or Emmy Noether, then they aren't doing justice to history.