Yes. Here are a few examples =
X-Card =
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"You are limiting my fun". Player A wanted to make some bad choice that would get them into trouble or even dead. By and large, this choice would not affect other player characters, or it would but only in a tangential way. Player B cast a spell on Player A's character to prevent them from making the bad choice, thinking they saved a life. Player A X-carded and said "I feel like I can't play my character by my own choices."
While we all know about the kinds of players who ruin the scene for everyone, or do actions that ruin the plots of others = this was not one of those times. So the use of the x-card seemed appropriate. We abided by the rules of the x-card, we did not debate, dither, or ask for justification of the X. We just altered play, let Player A fall to their death and moved on.
We had a retrospective after game and came to the unanimous conclusion this was a proper use of x-card.
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"You need a timeout" = Player A was highly emotional, and making demands that were no longer in character. They tried to couch their actions as their character being panicked over the situation at had (which as dire at most, and charged at least.) At some point Player A continued to halt play and demand alternatives or simply walking away from the scene.
While we knew the scene was pushing buttons, and we knew there were stakes on the line for loss or suffering. It was well elaborated on in the CATS agreements everyone made, that this was a goal, tone, and subject matter of the game. The player who had the X card imposed on them did not argue, they took a hour timeout and came back to passively witness the rest of the session.
We had a retrospective after game and all players agreed this was appropriate use of the X card, and Player A thanked us for not judging them, and just giving them time to chill.
Side note: many games later, Player A X-carded themselves and put themselves in timeout when they felt they were too emotional to play. This was an excellent use, as it required nobody to call anyone out, and it didn't impede play. They only needed about 15 min cool down time before they were able to come back and fully engage. They said it was great because the card helped ensure they felt they would not be judged or miss out, but also gave them the time they needed to handle emotions.
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OVERALL
Just like C.A.T.S.; we have found the X-card to get used 2 or 3 times a year, out of many many games - no not used often at all... but when its used it is a MAJOR help and respectful way to handle issues where players are being earnest but not on the same page.
We tend to see more value in C.A.T.S.; as that ALWAYS curtails players being on different pages. It was talked about, written down, and posted. So it tends to be a great silent way to remember what this particular game is all about.
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Side Side note
We tend to see these problems mostly in D&D, and a few other combat heavy, non-social rules, non-player agency, pass/fail games.
The more hopeless a player's dice rolls are, and the more GM fiat dictates fun - the more the X-Card and CATS is needed.
IMHO....Most everyone (not all) who join a player-agency or GM-no-roll game, tend to not need these tools as they are pretty well aware of the stakes and content of the game well before characters and sessions start...