I think it has more to do with the fact that when you offer zero salary for moderators, you have to take what you can get, and it ain't good. I don't really see a connection to the voting mechanic.
Why do you think it makes a difference if they are paid or not? Or more to the point: what are you saying? That people have different standards when paid? That lack of remuneration justifies poor effort? Isn’t that a very transactional view of human interaction? Are we that transactional? Do we want this?
We’re talking about how communities can become toxic. How we humans sometimes create an environment that is at odds with our intentions. Or at least what we outwardly claim to be our intentions.
I think it is a bit sad when people feel they have to be compensated to not let a community deteriorate.
It's also disconnected incentives. SO users get numbers to go up by taking moderation actions so of course they do that. Also you literally get banned from reviewing questions if you don't flag enough of them to be closed. These are incentives put in place by the SO company intentionally.
It's not like only slimy people get to use moderator tools like on Reddit, since you need a lot of reputation points you get by having questions and answers voted up. It's more like (1) you select people who write surface-level-good answers since that's what's upvoted, and they moderate with a similar attitude and (2) once you have access to moderator tools you're forced to conform with (1) or your access is revoked, and (3) the company is completely incompetent and doesn't give a shit about any of this.