I've seen it used plenty of times, sometimes in pretty bad ways and sometimes in perfect ways.
Back when I used to run games for money, I was giving a lot of questionable players a trial as part of the vetting process. I had one that would flash the X card when they were on the brink of being defeated in combat. At first it wasn't questioned, but there was certainly a fair amount of confusion. But it happened several more times, until we finally asked. They just... never wanted their character to be defeated. They weren't inherently trying to be stronger than anyone, but they never wanted to actually lose.
I've seen players use an X card against Charm or Dominate abilities - both in my own games and in other games. This was a major agency issue for them, even when it was done by enemy forces (as opposed to PVP). In some cases it was because the Dominate asked them to do something dangerous for their character (nothing sexual). In another case it was just being charmed in general, the idea that they had to act counter to their own wishes.
Arachnophobia has come up and been carded. This was my fault, I was being pretty vivid.
Dead children has come up and been carded. This was also my fault, I was NOT being especially vivid, but I did describe there being dead children amongst the other killed villagers after an orcish raid. They walked by the burning ruin of a house and saw one of the kids they had met earlier.
One of my players used it at a completely unexpected time, when I was talking about a lich consuming the souls of some innocent villagers. It was just a somber moment, and they needed to step away because they felt bad about the idea of a soul being destroyed permanently despite having done nothing wrong.
A similar story, I had a player break down into tears after I described an old grandmotherly woman forget the name of her daughter, simply because of old age. It hit a very personal nerve and the player apologized and X'carded themselves for a bit. We quickly moved past the scene while they had stepped away.
I got X carded once for mentioning that I was going to play a black character. I had no prior history of depicting anybody of the sort, and am strongly against racism in general, but the other player said they didn't even want to "go there."
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Of course, back in the day we never had anything like that, and there were so many problematic players. Countless moments where some kind of safety tools or CATS would have come in handy. From rapes where other people giggled about it (I sadly just sat in shocked silence, so shame on me). To guys playing women characters, but acting in completely inappropriate breasting boobily fashion. To players that just really clearly were enjoying the shock value of describing pretty horrific torture to monsters and their children.
I don't know, I might be the outlier here having seen so much shady crap, but I think many players have come so incredibly far in being respectful to each other compared to how things used to be. Or maybe I just don't spend any time with people like that anymore.