Bringing oxygen into our lungs certainly is important. I disagree that breathing, as in knowing how to take air into the lungs while performing a stroke, is the most important thing if one falls in the water. Staying afloat, so you can take oxygen into the lungs, is the most important part.
From the point of view of someone who was a life guard and who grew up around large bodies of water, swimming long distances is often the wrong idea when one finds oneself in the water. Being comfortable floating and treading water is important. Spending time in deep water is certainly one way to accomplish this. Yes, at 5'4", I can tread water and float in 5-6' of water, but the water feels different when it's much deeper and there's a psychological aspect, too, knowing that you can't touch if your get tired or a cramp or whatever. The strange thing is, even at 38, I can still effortlessly tread water for a long, long time.
Being able to swim long distances is one part of swimming, but certainly not all encompassing. Yes, it's a good skill, but not he be all and end all. My guess is in these summer fun pools, not many of the children are lining up to swim laps in an orderly fashion. They're playing games, jumping, wanting to dive, developing a familaririty with the water that's important.
My guess is that there are reasons beyond depth that your children prefer the community pool. Think about it.
Diving for objects may not teach you to breathe while swimming, but it certainly builds breathing strength. Mr. FourPeas was a very successful member of his swimteam. Very successful. He swam the long distance events. When it comes to treading water and generally staying afloat in deep water, I can do it for much longer and am more comfortable at it than he. We're both very strong swimmers and his breathing with respect to swimming laps is far superior to mine. He's spent much of his time in the water swimming laps; I spent mine "just" diving for objects and playing in water over my head. (BTW, I do occasionally swim laps, although now that I do it less frequently I can only swim for about 30 minutes rather than 60.)
I still say removing the deep end is a silly (and sissy) plan. It does our society a great disservice.