So many of them don't have arm bands? It's borderline criminal to allow untrained kids in a pool without wearing those.
Of course once they start swimming lessons, they practice without armbands.
In other words, if the small child supposedly needs armbands, they shouldn't be in the pool at all because the inflatables can easily slip off the arms.
Armbands are dangerous and hinder learning.
The only buoancy aids that should ever be worn are Coast Guard approved PFDs. Anything else does more harm than good.
You can get a great used wet suits for next to nothing, and in many cases the swimming pools have life jacket loaners. A life jacket with safety straps (between legs) are super cheap, and they are adjustable for better fit. Snug fit means they're less in the way. And they're harder to remove.
Generally certain rides in water parks, like fast slides or streams will require you to have higher levels of swimming training to go on if you're under 14.
My parents were wise enough to enroll me in a course so I got my "early swimmer" (seahorse, Seepferdchen) training by age 6; that doesn't make you into a good swimmer yet, but at least you know the basics. Then elementary school took over and I got up to the gold diploma by age 10.
By age 8 or so I already was a far better swimmer than my parents, who never had any formal training.
I remember my mom once refusing to take one of my friends with us swimming when I was like 8 or 9 because he didn't have any swimming diplomas yet (he had only come to Germany from Tunisia like a year prior and was in the process of catching up with swimming ed). I remember I was mad at the time, but in hindsight it was absolutely the right decision.
Still, we all knew stories of kids relatively close to us drowning; for me it was the little brother of a friend of my sisters who drowned when he went to a water park as part of a kids birthday. The "usual" had happened: the two parents of the birthday kid being too overwhelmed by 10 or so loud kids amped up on candy and not trained lifeguards anyway, not enough lifeguards, wave pool... the adults didn't even notice they had lost track of this one kid until they saw the lifeguard pulling him out of the water, too late, or so the story went.
[1] https://www.dlrg.de/informieren/ausbildung/schwimmabzeichen [German]
All swimmming instructors in those organizations will tell you that you should permanently keep an eye on your kids and don't let them go to the pool alone until they complete the bronze badge which requires you to swim for fifteen minutes, dive down to two meters and jump into the water. Only after you complete this test you are considered a "safe swimmer".
If there wasn't a lifeguard the above obviously didn't apply.