I had an x-card, I could've turned the game off and never looked back.

This sort of is the "X-Card before the X-Card was a thing" … next to "Talk about it".

You always have the option to leave, but if you're having fun every other way, and the thing you're uncomfortable with doesn't seem to be a major thing, skipping it, to continue having fun, and seeing the other (non-uncomfortable) story end would be better than leaving, wouldn't it?
In RPGs there is more stuff going on, and the players (which the GM is one of) are writing a story together. Saying "Please don't make emotional deaths a thing" or raising the X-Card in case of an emotional death on the horizon (which should be the same thing) is better than making someone cry at a convention.

Even if it were for me to "tough it out" to advance as a person, uncertain of whether I could take it, or have to break down, crying after ten minutes, I don't want to do that with strangers at a convention, but at my home, ideally with friends.