Signposts typically are set up, for strangers of that particular area (you might also call them tourists). Yes I can participate in a tourism-related activity also in my home town. Going “hiking” OSM considers as a tourism-related activity.
At the same time as a tourist, I can participate in activities not tourism-related. Like going shopping and even, the shop explicitly targeting tourists, still OSM consider it as a shop 
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sometimes I call them humans because the only locals have four legs 
More seriously, what is interesting about the signs I’m talking about (the ones that materialize node networks in the Netherlands, their equivalent in the mountains of other countries) are not managed by tourism departments but by infrastructure departments. The tourism departments focus on another type of routes, that loosely rely on this infrastructure.
Still, we map them with tourism=information.
My point is: if you want to exclude minor tourist attractions from the tourism tag, there are other objects which may need reconsidering too.
I don’t think that’s a good idea. Even giving a ranking of tourism attractions I don’t think should be part of OSM. As there’s no objective system of rating them. I might visit Paris without any interest in the Louvre. Though it’s a major sight.
There are services out there focusing on that, like wikitravel, wikivoyage, … I see no needs OSM should put any focus on it.
I would that agree that works of art are not necessarily just for tourists. The problem is that the change would cause a huge disruption to the existing tags. Especially since most of art mapped is accessible to the public.