Oh, it's not THAT bad.
You get the occasional heart attack or anxiety / stress type illness.
But think about it. When the plant is coming down around your ankles (and I've been there more than once), the stress level is definitely up. License Class has to identify that susceptibility, too.
Many times, I have put a simulator into freeze, had red faced, sweating, shaking trainees facing me - and then said,"Aren't you glad this thing has a freeze button? Calm down, breathe, and let's sort this thing out." I spend about a minute summarizing events and priorities while they catch their breath. Teaching them when it's time for a brief.
You're right - some learn to control their pulse, some don't. Some ROs and SROs work better with adrenaline, some do not.