Sure rank doesn't precisely pinpoint how skilled you are at any given time, but having default rank categories gets closer.
You don't have to give the player the option of setting the rank requirement.
In application you'd be setting a category based on the following default minimum requirements (arbitrary numbers):
#250,000+
#250,000
#100,000
#50,000
#25,000
(I'm not going any lower because I assume that there are much less players at these ranks randomly looking for multiplayer games outside of friend groups)
You could also allow players to set boundaries between requirements to exclude higher ranked players.
There could be the argument that this would fragment areas of the community in multiplayer, but I think it allows for a better overall gameplay experience.
And to be honest, there have been plenty of times when a #250K+ player joins a game with a bunch of under #10K players (or being generous, #50K) and makes the group wait (because we're not mean) only to quit immediately. This will help new players find games they can actually play in.
The point isn't to display superiority, but rather to facilitate a better gameplay experience.