But as for whether the correct usage is sexist:

I explicitly said that usage need not be sexist (the convention itself is to a degree), just that it's understandably annoying.

Do you think a significant number of people here actually regard one sex as inherently inferior to the other and signal that view by their choice of pronoun?

No, but they may, well, not exactly forget that female people exist, but something to me inexplicable happens that makes it look like they do forget that. I can remember only one specific example that led to a flame war, but then I'm male and it doesn't annoy me anywhere near as much.

And that's not even the issue. One time I was debating something with another poster here and started talking about an unspecified psychologist. I intentionally didn't use any gendered pronouns at first, but in the reply the other poster started using male pronouns for the psychologist so I made a point of using female ones in my reply, and subsequently both of us used them for the rest of the debate without either of us commenting on it explicitly. I don't think the other poster was sexist, let alone intentionally sexist, but once the male pronouns were used I simply found it impossible to think of my psychologist as an ungendered generic psychologist and I found both that and the fact that the psychologist should deterministically end up as male in my imagination just because of an artifact of language highly annoying. If anything I imagine that these and similar things annoy the female posters here a lot more than me.

But if not, then you are effectively claiming that the primary purpose of language is to be perverted into a weapon in political power struggles.

Languages primary purpose is communication, obviously. It undeniably also is a weapon in political power struggles and it should not be. I don't see how using the male third person singular pronoun as indeterminate gender third person singular pronoun either helps communication (as far as I can tell it obstructs slightly) or is power struggle neutral.