His leverage at the time of the trade deadline was that he:
1. Was one of the top pitchers in the game, and he was on the market available for via trade. Any team acquiring him would have been doing so under the premise of getting a limited number of elite-level innings out of him for 2024.
2. Was still under multiple years of team control (arb). Any team acquiring him would have been doing so under the premise of getting many more elite-level innings out of him for at least 2025.
3. Any team acquiring him would have paid a substantial amount of prospect capital to acquire him, with a price set by (1) and (2).
The risk to Crochet for pitching in the postseason is the fact that his arm has been taxed like it has never been taxed before... ever. So he's at an elevated risk for injury, as has been discussed on this forum ad nauseum.
As far as the leverage that Crochet had, he has to look out for his long-term health. While I think it's kind of bush league, players at some point have to look out for their own health at some point, and I would imagine that the players' association would be able to speak up for him