I'm pretty sure it has something to do with not giving players multiple spots in line when the arena gets crowded. Think about it. I own three controllers. A Pro Controller and two pairs of JoyCons. I would theoretically be able to go into a public arena, claim to the system that there are three players by having three controllers setup, save myself two spots in line, and always be in. I would never be not playing. It would be a bit unfair to those who only use/own one controller and take up no more than one spot in line. This decision seems completely understandable.
That being said, if it's a private arena, there should be no reason why one can't use multiple controller ports. If someone is to exploit the after mentioned trick and get caught doing so, they can be removed from the lobby. This is the type of stuff we get out of a rushed game. Many aspects of the game weren't planned thoroughly enough, and the overall quality as a result suffered. My hopes is that these quirks like the one you made this thread for will be resolved over time, but for a game that's been out for 22 days, we can only hope for so much.