Yes.[1] In particular your point about analyzing chords in isolation is spot on.

In “An Introduction to Musical Analysis”[2], Nicholas Cook says something that I have always considered very profound and applies widely, not just in music, which is

   > All notation is analysis

So whenever you write something down in music you are (of course) making some simplifications and you are also doing it for a particular purpose. Usually the purpose is performance. So when you write something you are providing an instruction to the performer.

So when you write Cma7 for a jazzer, that’s an instruction that you are generally in the major tonal area and they may well play a Cma9 or a Cma7#11 for example. This is why my functional harmony teacher used to get annoyed by people writing the “Crosstown Traffic”/“Purple Haze” Hendrix chord as E7#9 (which you see a lot). He would say it is E7b10 because that g natural is coming from the minor modes so it’s actually the fourth degree which has been flattened. If you call it a #9 you’re telling players the wrong scale for improvisation (pretty much everyone else in the whole world calls it E7#9 though).

Likewise going back to your point about slash chords, a lot of people learning this stuff get hung up on “what is this slash chord really?” (Eg if I’ve got B/C or whatever what actually is that) whereas when I’ve talked to really serious musicians in that world who play that kind of intense modal music they really are thinking about what the slash chords are in terms of where they come from and what they are leading to. Because that gives a sense for what the underlying tonality is. You can’t get it just from the notes of the chord vertically in that one instant.

If you look at baroque music and earlier, if you just do a vertical chord analysis (eg something like Gesualdo if you really want an extreme example) the chords make absolutely no sense in many cases but that’s because they work in terms of voice leading (ie context) rather than vertical relationships. Analysts used to call that feature “vertical false relations” because they found the vertical chord analysis troubling.

[1] ex-professional musician with a degree and postgrad in jazz, contemporary and popular music here. Wife is a professional musician who teaches at a couple of conservatoires and mostly plays baroque and early music with some 20th and 21st C music thrown in for good measure. Lots of pro musician friends. Not trying to argue purely from authority but I do talk music a lot with people who know a lot, and this topic comes up a lot.

[2] Which stands out as a great book in a field with lots of terrible books btw.