Mods are pretty clearly the nobles who landhold and collect taxes/etc. Not really a member of the court or the royal institution, but entitled (literally - Baron, Duke, etc are literal titles) and commissioned by the royal institution to rule over a small fief in the day-to-day matters.
The king wants the kingdom to run smoothly, and the baron makes that happen. If they do a shitty job they can be removed. On the other hand most barons won't want to let things get to that point, because it's still way better than being an actual serf (assuming they're not punished/executed).
And yes, many mods do derive personal satisfaction and power and influence (banning people they find particularly disagreeable, or particularly skilled at calling out a particular bit of bullshit the mod wants to push) in their work.
I've experienced the "you're banned on a random comment for no explanation, and if you modmail and ask why you're modmuted for a month instantly with no reply" personally as well, in a large discussion sub, over something completely innocuous.