Recently retired EMT here. You hit the nail on the head. For me, dealing with the patients was the easy part. I had one simple rule: just be nice and show that you care. Sometimes, that was the most important thing, especially with the chronic "frequent fliers" we were picking up nearly every day.

Coworkers were the hardest part, not just that they were jaded, but they actively viewed coworkers that did not ascribe to their jaded worldview as the enemy.

Similar experience w.r.t. patients (my coworkers were great though). It's really not about saving lives. It's about confidently telling somebody it's going to be okay when they are having the worst day of their life. That means the world to people.