We already do, and that causes problems, so we invented dentists to yank them out.

Yes.* They'll close off their gills and open their mouths, which creates a vacuum and sucks the food deeper into the mouth, then they close their mouths and open their gills to flush the water out but keep the food.

Morays on the other hand, have two little holes on the sides of their neck, and those are the exits for their gills. That's why they always look like they are gasping or yawning; they are trying to force more water over their gills.

*There are a couple different structures for biting and swallowing food in the fish world, but a lot of fish simply open their big mouths and suck in nearby prey.

That still isn't a purpose, but I guess a better example would be something that's useless to everybody. Like wisdom teeth.