These are some really good points. It is reminding me a lot of one of my favorite John Cleese videos[0].
One of the things that I think makes this so difficult is that language has a lot of limits that people don't realize. Since we often don't run into issues with communication (or rather don't notice since the errors are small) it is difficult to realize when we're in boundary cases. For example there's priming[1]. Many may learn that this is a useful way to influence people and many are aware of the psychological experiments, but it is also a fundamental part of how we communicate. We try to communicate the most information with the least amount of words. But this same factor is why good faith arguments are so important but also difficult to maintain. We could not easily converse if we didn't make certain assumptions about another person's views. This is normally fine but we run into problems in heated topics where we often act like someone can only hold an extreme opinion (and of course, mine is not extreme and just common sense). It's the "oh, I've heard this argument before" and while one person may have subtext another may not (why it is difficult to identify dog whistling). Removing nuance from a topic makes it easy, and we like easy things. But that's not beneficial to resolving issues and like you say "leads to a wilderness of mirrors".
But it is impossible to tell if priming like this is actively being pushed or naturally happening, since we do have a natural predisposition to form tribes and groups. We're nuanced and thoughtful with our arguments while they are overly simplifying and idiotic. They just want a win while we want to actually fix things. And since this kind of talk is natural it is also almost impossible to figure out if I'm doing the thing I'm actively complaining about or not.
I like Monty Python so I watched your Cleese video. It's funny, but of course he lets "moderates" off the hook as if they aren't just as subject to this dynamic as everyone else, when the truth is that they not only are, they have the ace of trump cards—social proof—to mask it with.
To me the interesting thing about that video is that it shows how much self-reflection (or personal work, whatever you want to call it) Cleese had been doing by then. His classic character was the rigid, angry type who was comically un-self-aware, which had roots both in his own character and also in his effort to be conscious of it—it takes consciousness to make oneself hilarious in that way. In this video, the way he describes how to feel good about yourself by projecting badness onto others shows how much deeper he had gone with that.
At the same time, with the blatant loophole for "moderates" in that bit, one can sort of see his limit.
I think the conversation about moderates has changed a lot in this election. I think this also is relevant to our "no nuance" conversation. Defining a moderate now is relatively difficult and I think more people think they are moderates than actually are. Are we talking about moderates from a fairly objective viewpoint? American standpoint? That of the state? Are we talking about the moderates that the DNC describes and are the Joe voters? Are we talking about the moderates that the RNC describes? The moderates of today or the moderates when that skit was written? While I agree with you of the loophole of moderates since many self-label as moderate (even if they aren't by any reasonable metric) as a means of "feeling good" and having moral superiority. That kind is the same pitfall as the extremists, but I think just lumping all moderates into that bin (and subsequently having a total of 3 extremist bins) isn't helpful and makes it difficult to heal the divide that we have.
That said I'll admit I have a bias that I'm against parties since I feel they make things too simple for a well functioning democracy but you've also probably seem my passionate comments about voting.
One of the things that I think makes this so difficult is that language has a lot of limits that people don't realize. Since we often don't run into issues with communication (or rather don't notice since the errors are small) it is difficult to realize when we're in boundary cases. For example there's priming[1]. Many may learn that this is a useful way to influence people and many are aware of the psychological experiments, but it is also a fundamental part of how we communicate. We try to communicate the most information with the least amount of words. But this same factor is why good faith arguments are so important but also difficult to maintain. We could not easily converse if we didn't make certain assumptions about another person's views. This is normally fine but we run into problems in heated topics where we often act like someone can only hold an extreme opinion (and of course, mine is not extreme and just common sense). It's the "oh, I've heard this argument before" and while one person may have subtext another may not (why it is difficult to identify dog whistling). Removing nuance from a topic makes it easy, and we like easy things. But that's not beneficial to resolving issues and like you say "leads to a wilderness of mirrors".
But it is impossible to tell if priming like this is actively being pushed or naturally happening, since we do have a natural predisposition to form tribes and groups. We're nuanced and thoughtful with our arguments while they are overly simplifying and idiotic. They just want a win while we want to actually fix things. And since this kind of talk is natural it is also almost impossible to figure out if I'm doing the thing I'm actively complaining about or not.
[0] https://www.youtube.com/watch?v=HLNhPMQnWu4
[1] https://www.psychologytoday.com/us/basics/priming