Citizens do not trust that the government will maintain and police them properly, and I think the homeless and sanitary situation in San Francisco is a perfect example.
In contrast when I lived in London I always felt access to public toilets was pretty good. There were lots of places like McDonald's, Starbucks etc that always let the public use their toilets for free. Then there are free toilets on many large rail stations past the barriers as well as paid toilets before the barriers. Finally there are free standing paid toilets dotted around the city. Back then one had to put a coin to open them.
Personally I think London is one of the better European cities in this regard.
This is the problem not NIMBYs, It is the correct assessment that the bathrooms will not be policed or maintained. If they were policed and maintained, no one would even notice them.
Sanitation is one of the main things we need a government for; failure here is unacceptable.
Would they rather have toilets that cost a dollar to use or no toilets?
It's probably complicated at this point in that I assume most people in the US don't carry change today and tap to pay small amounts is fairly nascent.