In a regular day-to-day dojo enivironment, the choose-your-partner concept is reminiscent of those miserable phys-ed classes in junior high school and high school, where the designated outcast always found him/herself being the leftover when the appointed "captains" were allowed to pick their team. Some might say it's how kids learn about "life" and the law of the jungle, but I find it loathesome.
...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.