To what extent did medieval bath houses prevent disease and illness?
Recently I've been doing some worldbuilding, and something I've ran into while trying to "reduce" mortality rates in an early modern setting is trying to understand the relation between disease and "sanitation" so to speak in previous periods. One of my initial assumptions is more access to public infrastructure like bath houses would reduce mortality.
My (mostly european based) understanding is that in the medieval period people did wash their hands (though not necessarily often with soap or replaced water), bathed when they could (though for most not often with hot water), and knew not to drink from stagnant water. And part of that sanitation was the use of bathhouses. My initial guess is that this still doesn't necessarily deal with contaminants you can't see in flowing water, hence the importance of germ theory in sanitation to reduce mortality.
Going back to bathhouses more specifically, there's this series of answers collected by u/Vir-Victus, which note issues with Roman bath houses with water replacement, intestinal worms, and warm humid environments. And I've seen it noted that bath houses may have declined after the medieval period due to connection with the spreading of diseases like syphilis through prostitution and other means. This provides for the before and after period of medieval bath houses, but not much of the in-between.