Net-Chess.Comhttps://www.net-chess.com/phpBB2/

When I went to investigate 2 other sites, chess.com and chess24.com, I discovered they incorporate this feature.
Namely: if you do not want to play with the person you are matched up with, for whatever reason: too weak, too strong, you've played that person before and didn't like his/her attitude, you can simply abort the game without losing points, and move on.

I will confess that there are some people here that I do not wish to play with.
If I post a 2-person match and one of them signs up, I'm stuck.
If it's a more than 2-person match I can always Unjoin before it's filled, but...you never know who the last person to sign up
is going to be and you're stuck with it once again.

What says Greg and anyone else?

There's no abort for tournaments on Chess.com. You can withdraw from a tournament and forfeit your remaining games and not lose rating points, unless it's a thematic tournament of more than 3 moves when you will lose points.

I've seen this abused quite a bit on FICS. People use it to abort games when they don't like the opening move, or as an alternate method of filtering players by rating when there's already a method to do that.