You just described exactly why I consider the term problematic.
Mind you, I don't personally take issue with the term when used, although I'm able to comprehend why others do. It's why I use quotation marks when I refer to it (to denote that I am using terminology and distinguish it from the natural use of those words). I actually enjoy engaging in "skilled play", I just think that it's a bad, loaded term, and I would never refer to it that way outside of something like a D&D message board.
I don't know. I think it is just a handy term. Obviously you should use whatever terminology you are most comfortable with. I have never really encountered anyone taking issue with it outside a handful of discussions on this forum. To me it is just a positive descriptor. Lots of play styles use them because people are enthusiastic about their style and the terms they adopt early on usually reflect that. To me its only a problem if the people playing the style find it insulting. For example if people who like to optimize were adamant that power gaming was an insult and they didn't use it themselves I don't think I would use it to describe that style of play. However what I wouldn't do, is automatically a assume that a person who is describing their game as a 'power gaming style' in any way means my style must therefore be weak. I get that they are using the term to invoke a certain set of ideas and then they can explain specifically what they mean when they drill down. But power gaming, skilled play, optimization, people who play styles that place a premium on character agency, freedom to explore, etc, are just useful plain and simple English to describe a style. The advantage of them is they don't sound like overly academic or obtuse terms, which is why I prefer them. They just kind of cut to the heart of what the style is all about in a clear way (sometimes being playful with language----which I think there is nothing wrong with). I find what often happens when I enter these discussions is rather than even talk about the style we spend pages and pages dissecting the terms, and once those terms are dissected and taken away, I just personally feel it is a lot harder to even try to convey what I mean anymore.