The problem with that is that you can be manipulated into causing harm by a malevolent actor. All they have to do is threaten some greater harm, and you become their tool, which can increase their power and their ability to threaten larger harm. “You must go out and kill one person, or I will command another of my agents to go out and kill three.” This essentially precludes standing up to any powerful entity in any meaningful way.

Refusing to kill one of the hostages, or pull the lever to run over Palestinians, leaves open the possibility of forming a united front to defeat the people forcing us into such situations in the first place. Keeping one’s own hands clean is not simply a matter of “moral purity,” but rather, an intentional strategy of avoiding actions taken against a particular group.

No, those are separate problems, not the trolley problem.