I know it was a huge step forward, but:
1. The constant flow of water need 2 things (Aqueduct, or spring, and evacuation system) Without these, it's just a a pool, as you said.
2. In game terms: Sanitation allows to build Public baths AND Aqueduct, so you're right, it's an indicative of of how hygienic a civ is. But they are not build at the same time, and are you sure you build an aqueduct in every city where you've built a public bath? The bonus of 2

when the aqueduct is operative compensate(sorry if this word doesn't exist, english is my third language) the 1

provided by the public bath.
3. Rich and healthy people don't goes in public bath, they got their own baths. If not, there were special rooms for them in the public therms for security reasons. The rest of the people bath together, without no one to control if they are contaminated with scrofula, papillomavirus, or another contagious disease... You can replace water every hour, those who are together in the same pool at the same time risk contamination.( not to mention those who urinate in water, or worse...)
4. In modern world, with chlore, antiseptics, and so on, we still fear plantar wart when we go to the swimming pool, or the shower in sports clubs,...
These, plus a lot of reasons that I'm not really able to write in nearly correct (?) English, make me think that the 1

penalty is correct.
Even more correct if they have sex with public women near, or in the water...