Ultimately, I think it's very difficult to choose to work a job that requires firing people and still be a good person.

Iiiii really disagree. Sometimes, people are bad at their jobs. There can be all kinds of reasons; some can be worked with and some can't. But situations in which an employee is, for whatever reason, not doing their job, or doing it so poorly that the other employees have to redo it, pretty much always become untenable at some point.