"MT Melissa Greenhagen was shot in the back by a sniper in a hospital parking lot."
All the carry in the world wouldn't have stopped that attack.
An acquaintance of mine is an EMT. He's pro-gun, but says carrying on the job is the last thing he wants to do on account of the frequent physical interactions with patients, both cooperative and non-cooperative. He doesn't want to have to worry about a possible gun grab. He says on most responses, there are other big, burly firemen out there to help subdue an unruly patient. If the patient is armed or otherwise dangerous, they usually don't require immediate treatment, so they back off, let the LEOs do their thing, then re-engage.
Then there's the fact that the primary job is to administer medical treatment, and that some patients have a genuine fear of firearms. It's like when we have extended family get-togethers. I don't OC then because a few are opposed, and it's more important to me to facilitate the family get-together and maintaining good relations with my cousins, aunts, uncles, nephews, and nieces than to prove a personal point.