I almost mentioned Hooters, I think they're the exception that proves the rule - they're seen as unusual and seedy, whereas in Japan that's pretty much the norm for a bar.
"the exception that proves the rule" is such a terrible expression. I do not understand why people use it.
At some point I thought that it absurd on purpose but I had some people explaining me the rationale behind it (there is no rationale - if there is an exception it at best weakens the "rule")
‘Prove’ was historically used as a synonym for ‘test’, which gives the phrase quite a different meaning. Like how ‘result’ is now sometimes used to mean ‘positive outcome’, as in a football fan saying ‘we got a result’
The expression is referring to an implicit or unstated rule. Defining it is hard but people know when it has been broken. Hooters is an exception, the rule is, don't be like Hooters.
Just as you say, the point is that a rule is implied by a specific exception, as in the example "free entry on Sundays", which implies the unstated rule "pay for entry on other days".
The exception weakens the rule, it's true, but may also reveal the rule.
It’s a folkism, but consider this: If a rule doesn’t have any exceptions, is it really a rule? If a rule doesn’t exist how could there be any exceptions?
The norm for a bar in Japan is to be like Hooters?
Eh, what? This wasn't my experience at all. I didn't conduct a study, but I was in a good few bars over there, in three different cities. Can you elaborate on what you're referring to here?
In my experience a bar (not a pub/居酒屋, a バー) will frequently be a place that always has female staff working, where those staff will be wearing makeup and at least somewhat attractive clothes and expected to converse with customers. Not always - there are definitely bars focused on music or some hobby or particular kinds of drinks - but often enough that it's what I'd expect if you just said bar.
Think the takeaway was more about the "seediness" aspect of Hooters do to it's being pretty exceptional/unusual in American dining culture.
Hooters is a pretty unique restaurant experience in the US and is therefore considered different/further from the norm and frankly by many seedy. If there were more places like Hooters in the US then this would probably not be true.
The comment was trying to explain that in Japan you have a lot of places that would be analogous to Hooters in the US...so it's not exceptional/not seedy. Maybe not quite the "norm" but common enough to not be really something that gets noticed or have a connotation like "seedy".
Japan has (had?) an exact analog to Hooters, namely "sexy izakayas" like Hanako, where pretty girls in very short skirts serve mediocre bar food. These were pretty much obliterated by COVID though, and were always a small niche.
Unlike the US, Japan has a highly visible and de facto legal sex industry, so if anything sexy izakayas are/were at the less seedy end of the scale.
At some point I thought that it absurd on purpose but I had some people explaining me the rationale behind it (there is no rationale - if there is an exception it at best weakens the "rule")