I've always found of the X-Card to be a tacit admission that those people most invested in calling for one don't see the other people at the table as people worth talking to, nor do they see them as people who have responsibilities for themselves.
I run an explicitly unsafe space. I like to make that free and clear to everyone at the table when they sit down. Things you don't like will probably happen. Things that disturb you will probably happen. That you feel disturbed is no reason to stop the game. That you feel "triggered" is no reason to stop the game. That being on the table, you are going to be sitting with some people among which can be an asshole.
If everyone's playing and having a good time and then out comes, "the eight hairy legs of the hideous giant spider creep over the edge of the long forgotten well, it's sparkling, beady eyes full of ravening hunger and its hideous pedipalps clash noisily, breaking the silence," and just last week you'd fallen into a nest of brown recluses and really would rather not be reminded – then it's incumbent on you to say "dudes, I am really not down for the spiders today. Last week's nest full filled my quota. I'm just going to step out until the end of the scene, have a bite of pizza, and someone come get me when the stomping is done." And then get up and do that.
Now, if you explicitly told people that you were about to run an old-school dungeon crawl and they didn't expect spiders to pop up along the way – that's on them. They should know better. It's incumbent on them to look after their own interests.
The real problem with the X-Card as a construct is threefold.
Firstly, it puts the burden for dealing with the situation on everyone but the person whom that situation falls on. Everyone else suffers. Everyone else is expected to suffer. Everyone else is expected to suffer cheerfully. The responsibility falls on everyone else at the table.
Secondly, it explicitly maintains that explanation is not really necessary. It creates a blind behind which any motivation suffices. That's a terrible situation to put forth.
Thirdly, it infantilizes everyone at the table. It makes the assumption that they are not strong enough adults, not self caring enough, and utterly not socially adept sufficiently to be exposed to a thing, make a face, and say "dude, what the fuck?"
The assumption that negotiation is not possible and thus needs a tool like the crowbar to open up the gaps for it is the part that I find most personally insulting as a gamer. It makes me wonder about how these people have been communicating about their games – effectively forever.
But since most of these individuals seem to have an issue with personal responsibility and personal accountability in the first place, pushing an individual's problems out on all those around them and leaving them with no responsibility, I suppose I shouldn't see much of anything that gives me surprise.
In my other answers to @grimjim's post I already shared my opinions to most of your points, which in the end aren't that different (X-Card abusers, conventions, not trying to be the guy making someone cry at your table, …)
However
Summarizes the whole X-Card-debate pretty well:
The X-Card should not replace proper communication, but the X-Card is (or should be) a shorthand for everyone to say (especially to the currently talking person)
"I do not want the thing that is happening right now. Are you all alright with changing/skipping the narrative, or should I explain myself for a second?"
It should then be everyone else evaluating "Am I alright with nodding this off, or does this spoil my fun, in which case I should talk about this."
Often however some people say "If someone raises the X-Card the current thing HAS to be skipped, no questions asked!" which doesn't talk about the problem, not solving it. The whole RPG is a conversation, people should talk about it.
If someone isn't happy you should talk about it.
Don't forget to talk about stuff. Talk about why you used the X-Card. Talk about how you intend to carry the game on. Talk about the other players opinions.
Talking about things is often forgotten when talking about the X-Card.
The problem from where I sit is that "the X Card should not replace proper communication" is what a lot of people *say,( but when you look at what they actually do – it's not a shorthand, it's the only hand.
Why do you need shorthand for a two second act? Seriously. A reasonable adult should be able to hold up their hand, point at the GM, and say "hold up, I'm uncomfortable with this," or point at someone else at the table and say the same thing. Then they can have a discussion.
Unfortunately, this gets coupled with "anyone that's uncomfortable should never have to explain themselves," which is a toxic combination. That idea is toxic to communication in general, anyway, but in combination with a clearly defined trump card (irony utterly intended) it actively impedes the conversation at the table.
I much prefer to disengage the whole thing up front. If I wanted to run a game for kindergartners, I know where the local schools are. Of course, the local kindergartners generally have a better grasp on how to play together that a lot of adults, especially in the RPG industry.
The shortcut shortcuts conversation. It actively impedes communication. Especially in combination with a lot of the other rhetoric which comes out of the mouths of the people who espouse the X Card, it's actively pernicious and damaging.
Screw that. I don't need that kind of static.