There are lots of pools in almost every major city for example:
New Yorks 5 Boroughs are home to: 34 outdoor pools, 12 indoor pools, 24 wading pools, 19 mini-pools and 5 diving pools
Chicago park District has 26 indoor pools and 51 outdoor pools
St Louis has 3 outdoor and 5 indoor pools and the indoor pools are open year-round and offer free swimming and free lessons to everyone.
Even if your town had 75 pools and they were all free, the big presumption is that the parents can take the kid to the pool.
My mother worked endlessly and thru illness. My mother did not spend her summers by the pool with the kids--she was working and so too was my dad.
Yes, I guess you can say, kids go to the pool and let the guards take care of you--I guess--but I would think that would be a tad of a problem.;)
Time--if you need to make money to buy food and clothes your kid, that is your priority--working and where your time is spent.
That was just my experience.