Do you think wrestling shoes would make much of a difference in sparring though?
Difference how? For the person wearing them or the opponent?
For me, it didn't make much difference. I got used to the difference in grip on the floor and weight within a few minutes once we started the kicking part of warmups. I always hit the heavy bag wearing running sneakers, and there's not much of a difference there either.
I take them off during sparring because that's my CI's rule. His house, his rules. I don't know how they'd fit under the foot pads we wear. And as Gerry mentioned, the biggest issue would probably be scrapping/burning someone's skin with the sole if they were to get hit with a glancing kick from a front kick or side kick. Maybe the point/toes would hurt more if they'd block on that spot with a forearm.
Realistically speaking, I don't think it would make much difference getting hit with me wearing them vs not wearing them. My CI probably feels like why take the chance of someone getting hurt in an unforeseen way that could've easily been prevented.
I don't wear them often; maybe 3-4 weeks total for the year. It's not like sparring for 20 minutes without them on is going to make or break my foot pain. If that was the case, I wouldn't be on the floor because it would be time to heal up instead of pushing it. During non-sparring stuff, they help a little bit. They're far from being properly supportive like my Nike Air Max shoes. But every little bit helps.
My main reason for having everyone wear them in my hypothetical organization is so people don't transmit stuff like athlete's foot, plantar warts, etc.
All I know for sure is I like training in my Asics Mat Flex shoes more than barefoot. They give me a little more support, are a little more realistic, and keep my feet from cramping up.
But there's the whole traditional white gi and barefoot thing that I like too.