...except that we're adults. Right? Seriously, do you think this is typical in a "choose-your-partner" dojo? Adults can generally function without creating "designated outcasts" like a bunch of attitudinal tweens.
As OP describes this dojo, I don't think that removing the "choose your partner" option would make things any better. Sounds like a pretty broken place.
Yes, we're adults. And yet, I have seen this behavior at other dojos and was even subjected to it. Adults can act alarmingly like overgrown kids on the playground. Age does not necessarily correlate with maturity; insensitivity can last a lifetime. Adult cleverness just allows older folk to come up with pretty words and excuses to rationalize childish behavior.
I wasn't stating that this is how the OP's dojo should be run, nor did I say that the round-robin method of training will cure a dysfunctional dojo (and, I agree with you that the OP is describing a dysfunctional dojo), but it may instill civil behavior. These people apparently were not taught basic manners and inclusiveness as kids, and perhaps the rote "forcing" of civility will at least cause them to wear the veneer of civility.
But if the OP can find a better place to train, that would be the preferred option, in my opinion.