I can honestly I've never had any particular desire to 'touch' underwater creatures. But, I have done some things that were, in hindsight, a bit foolish.
Quarries with brim and bass - and lots of divers - serve as great opportunities for fish to 'check out' the divers. The fish seem to be attracted, possibly looking for food, possibly just curious. A couple of years ago, I was working with a group of OW students hovering over a platform in one of our local training quarries. The brim were so thick that I was actually having trouble seeing my divers clearly. When 10-15 are right in your face, they can really obstruct your line of sight.
So, I thought I would 'perform' for the students, and I started poking my index finger at some of the brim, in no small part to get them to turn away from my finger so I could see (but, yes, I could be rightfully accused of showing off). I was also trying to show the students that the fish were curious but not threatening - that they aren't dangerous (to divers) UW predators. I had even briefed the students that fish will sometimes nibble their neoprene but it was 'no big deal'. Live and let live, underwater.
Well, the water was warm, I didn't have gloves on, and I poked at a brim to get it to move - and the fish bit my fingertip! Now, that isn't particularly serious, the teeth are tiny, and the risk of infection, even disease transmission, is inconsequential. But, the bite IS sharp, particularly when you're not expecting it, and I pulled my hand back (very) sharply. I could hear my students laughing (at me) through their regulators, and I thought a couple were going to spit their regs out, they were laughing so hard.
Lesson learned, I now resist even that tendency to 'touch'.