When the UFC was new, I remember reading that they wanted people to wear their style’s traditional uniform. They didn’t require it, but they wanted that visual to reinforce the style vs style thing. They asked a wrestler to wear a singlet, but he refused. He said he didn’t want to give Gracie an easy weapon where he could wrap the shoulder strap from it around his throat. I could be wrong, but doesn’t wearing your own gi give you a bit of an advantage in that you can grab your own sleeve during some chokes and the like for a little extra leverage? I’m quite sure that advantage is easily outweighed by the fact that your opponent can grab it too though. Regardless, in the earliest days, they were selling the style he style aspect of the event. What better way to reinforce that than having gis, wrestling singlets/trunks, boxing shorts, etc.