Flotation devices have no part to play in teaching how to swim. Parents (or teachers) holding their children and teaching them how to float is step 1. Only after the child can handle themselves in water (float, know when to breathe) should they be playing with flotation devices.
Previous attempts to teach me to swim used flotation devices. Without them, I was terrified of drowning.
A very smart swimming teacher, seeing my fear, taught me to float on my back, first with her assistance, then without it. Once I could float, she taught me to swim backwards, froggy style. I was afraid even about that, but she said "If you ever find yourself unable to swim, just float!" and I felt confident to do that.
From there, I was comfortable swimming on my front, because once again, I knew how to go on my back and float!
Then the rest was simple skill acquisition.
30 years later, I wish I knew the name of that swim instructor!
And one skill that swimmers need, but cannot really get with an float-assist device, is putting their face in the water. I watched an adult friend learn to swim, and this was REALLY hard for him. Crazy enough - he was ex-Royal Navy submariner, so he had passed basic water survival - he could float on his back, just couldn't do anything beyond that.
You can’t swim with a lifejacket. You can only float (and in a position that is different from how you would naturally float in water).
We used kickboards for this exact purpose. So you can float face down with arms outstretched holding the board. You can transition to freestyle swimming taking one hand off the board at a time.
They lack the failure mode of floating face down in water, but instead are unsafe to others who can be hit with them. And kids will collide.
The newer foam ones are much softer and safer.
As an anecdote, they almost killed a friend's daughter a few years ago.
She had jumped and fallen forward, and her arm floaties moved her buoyancy to her stomach-area, forcing her face into the water. Scary stuff.
She was even in a swimming pool she could stand in.
Also, when I was a lifeguard, one of the things that was sometimes hard to get to parents' heads is that "supervising" a non-swimmer does not mean sitting on the side of the pool reading a book--it's being in the water no more than an arm's length of the nonswimmer. Every second is critical in a drowning incident, so having a parent less than a meter away will almost always do a better job rescuing a kid than a lifeguard in preventing an accident
The reason for worn (handheld is a different story) flotation devices other than lifevests is to sell flotation devices; I've never found anyone who teaches swimming to children (or adults, but that's not the market for them anyway) that uses them, advises using them, or considers them anything other than a safety hazard.
If you want to get a kid used to “preswimming”, which as I've seen it is actually something mostly done with infants and toddlers (older nonswimmers usually seem to go straight from wall exercises to supervised short swimming with knowledgeable teachers) it's best to do it with an adult holding them, except for extremely brief transitions.
They are just often misused - you are supposed to be supervising them when they are in the pool period and they only need deep enough water to keep their feet off the ground.