I think it's perfectly fitting if you are going for a cultural victory. On a broader note, I find it cool that, in addition to turning mountains into Ski Resorts, you can do multiple important things with mountains in this game, which feeds into the bigger point of the map tiles feeling more important than in any other Civ game.
Yeah, I definitely like there being something to do with mountains late in the game, it's a new twist. But I do feel that they're so easy to spam, that it ends up being just a ski resort on literally every mountain.
I think it would be better if instead, a ski resort, say, covered the entire mountain range it was in. Even if it still takes a single builder charge, basically you build a resort and you get 1 tourism per mountain in the range. Ideally, maybe you allow people to share a mountain range, in case if a mountain range is in 2 civ's territory. That way, if you're using it for tourism, then a lone peak will only net you 1 tourism.
I would also suggest that for the amenity, you probably need that to come from a different source. Maybe that would be something for the airport - so an airport gives you +1 amenity if there's a ski resort within range of the city? Or maybe the airport becomes a regional bonus - every ski resort within 6 tiles of the airport can now provide an amenity to their closest city?
If you did that, then you would still spam ski resorts since they give you tourism for tiles that don't give it otherwise, but they're not going to be a big source of tourism unless if you have a big mountain range. And you're not just spamming them for an amenity, unless if you invest in building some infrastructure near them.