I also doubt it happens often. These guys and girls are tough, that's why they chose that job. Another problem is shock takes a bit to kick in. After the adrenaline wears off and your brain starts processing stuff, that's when things hit you. I saw a guy die once only feet away from me. Not a natural death, a messy death. Right after I wasn't freaked out. A few hours later I was pretty messed up.
You are absolutely right and that's something that I had not thought of until you brought it up. Adrenaline is one hellofa drug but when it wears off you come crashing down hard.
Regardless, being mentally unstable because of relatively normal events you endure while doing your job is not a valid excuse. It is something that we should encourage them to recognize and properly deal with though including giving them whatever tools and latitude necessary.