It's also a nice facsimile of swimming in a wetsuit in that it gives your legs some of the same buoyancy. It gives you time/energy to ponder and improve your stroke. As for not looking silly--triathlon gives you endless opportunities for looking silly. Go with it. And there are other people using equipment at pools, so people don't notice as much as you might think.
"My predominant feeling is one of gratitude. I have loved and been loved;I have been given much and I have given something in return...Above all, I have been a sentient being, a thinking animal, on this beautiful planet, and that in itself has been an enormous privilege and an adventure." O. Sacks