Originally, at least in Milwaukee, the natatoria were built to give citizens access to bathing and showering facilities, since very few people had such luxuries in their homes. Cleanliness was clearly deemed to be of great importance and had only in recent decades been tied to diminishing disease. Unfortunately, they didn't figure out right away that starting out with dirty water or admitting people in all states of health and ill health did not contribute much to improving disease statistics.
In any event, natatoria became quite popular and eventually changed into a source of recreation than cleanliness. Though many of the original buildings gradually closed or were re-purposed, the idea of communal swimming pools has never since then left us.