I think it is less that KYM "wants" to be toxic and more that KYM fails to acknowledge the very flaws it calls out from others, with the most obvious example I can remember being this post. The second top comment is MrLake calling the site "the least self-aware site in history" and, honestly..? He may be right: that was the second time that image was posted, after all.
Reddit is aware enough of its Reddit moments to meme about it, 4chan is aware enough of its Wojak problem to call it out on multiple boards, and even on Twitter, Twitter takes often get ratio'd by people with better common sense. But KYM, though..? It calls out everything wrong with politics while having political entries on the trending entries all day long, and trust me, that is not the frontpage's fault. Tik Tok stuff gets frontpaged just as much, yet it rarely occupies as much time and space on the trending tab as politics do.
The problem you mention is the result of the aforementioned self-awareness going unchecked and mostly uncalled for too long, and the reason for that is, I suspect, simply because we are not a "community" in the traditional sense of the word. No, we are less a community and more just a random bunch of millennials who happen to enjoy similar digital media in our laziest hours of the day. As a result, nobody here feels obligated to care about others beyond bare minimum interactions (and those who supposedly should… well, see your own remark about the air of only cynicism being good), and when the things that keep being pushed forward are mostly politics, those minimal interactions naturally become hostile as time goes on. Indeed, we are a lot less "civilized" than some people have pictured this site to be, not because of being Twitter levels of stupid, but being Twitter levels of reactionaries. Almost all talk and discussion here is a reaction to something that ticked someone off the wrong way, from a literal one user to the very US President himself.
You used to have fun here because KYM used to be the kind of site where the most popular and unifying thing people had in common was a cartoon about magical horses, and the second most popular thing being the random memes of the time, like 60's Spider-Man. Today, the most common things are politics and lewd images, and people over time found a way to fight over both at this point.
I am sure nobody will believe me on this one given my amount of activity seen, but this is mainly why I heavily lowered the amount of time I hang out here compared to my first year, being like a cumulative hour/hour and a half per day on average. In fact, what I enjoy the most here is the rare, but welcome DMs I sometimes get from people who want to talk about random stuff, either asking for my opinion or simply a point of view. It is only on those where I feel like I am at leisure talking, not worried about anything else but the conversation, being the closest to a "human" interaction I have gotten here, since all other public comment spaces here have gotten more and more dense or even tense, as you imply.
So yes, to summarize this overly long point I am making, the fact that we are just a bunch of randoms on a meme site with no real motivation to be more than that has taken its toll on our overall care for being… "nice", to put it bluntly..? Or at least less cut-throat about it, as you put it. It sucks if you expect a community feeling from here, which I honestly doubt many people seek from this site anymore, hence why it goes mostly uncalled save for the occassional post like this one.