I don’t think the X-Card encourages reckless play. I think reckless play is something that arrives externally, and can influence the way people interact with everything at the table, including safety tools.
I once had a game that moved into very uncomfortable territory that I, for one, was not comfortable with. (Monsterhearts, and I was MC’ing.) We stopped / slowed down when it happened, and then followed up with more conversation after the game. At the time, the player whose character had gone places we didn’t want to go, made a reference to, “Well, somebody could have X-Carded.” That said, I don’t believe that they were deliberately playing to the X-Card. I think that the issue would have come up regardless, based on the subject matter of the game, the particular narrative elements that were already in place, and the personalities at our table. I do, however, now include a, “Just because it’s there doesn’t mean we have to play to it,” disclaimer when introducing the X-Card.
Also, to be clear, I think everybody was behaving in good faith at our table, and the player in question really was just following the agenda and principles of their character and the story. We were a D&D group playing our first game of Monsterhearts, and just hadn’t ever needed to think about safety in those ways before.