I have heard of these and I have seen clips from them. I have not, would I ever utilize the class. I get and agree with the premise of teaching kids water safety, how to swim, and a healthy respect for the water (both the fun and the danger of it). I can't imagine just "letting them go" and see if they swim.
My son has always loved the water and was never fearful of it. He started swimming early, independently around age 3 but played easily before that too. We always joked that he thinks he's part fish. He is now a lifeguard (and turning 21).
When my daughter was born, we already had a pool. We allowed her in all the time...in our arms, on a raft, in a ring, whatever. Once she slipped in (when we were out there with her but no one was swimming). We didn't freak out, we calmly reached in and pulled her out. She has always loved the water, played and swims freely. Each year since she was just a baby, she was getting better as the season went on. Basically swimming (not quite independently) at age 3.5., starting independently at 4.5, and started this season on her own. I strongly believe that if we lived in a warmer area I am sure she would have been doing it sooner. We joke she is part fish or mermaid.
My point is that neither had a swim lesson but both were taught to have fun and respect the water. I taught both to float on their backs. I have told both how if they were in trouble and couldn't swim/needed a break and/or no one was close, float on their backs so not drown. And most importantly to not swim alone or without an adult and to remain calm. I am not a strong swimmer but I didn't let that hold them back (and I do enjoy the water).