Why are basis transformations written in order reverse to that of conjugation?

Question

Some time ago I posted a question here asking about the distinctions between the conjugation notation in group theory ($gxg^{-1}$ vs $g^{-1}xg$). I was under the impression that these are simply two different kinds of non-conflicting notation, but it was explained to me that the former defines a left action, while the latter defines a right one, so it's a matter of what kind of "orientation" one prefers. As I understand it, a significant portion of the mathematical community prefers writing functions before arguments and left actions, and, by that same logic, the former kind of conjugation. So then why are basis transformations usually written as $P^{-1}AP$? Isn't a basis transformation simply conjugation in $GL_n(k)$, why should it be written in the opposite order? I have seen authors write "left" conjugations and "right" basis transformations in the same books, why wouldn't this be inconsistent and conflicting notation?