Meh. Totally different than free solo'ing cliffs, where you have zero safety net.
To take a term from the tactical realm, it's all about your TTPs: Techniques, tactics, procedures. Not so much bravado. The prevalent personality types are P-F.com nerds and high functioning autists, not jocked out adrenaline junkies. Engineers, doctors, and technical types in general are over-represented in the cave community compared to most other hobbies.
Lights? Minimum three.
Getting tangled in line? There's specific technique to laying line which prevents this, as well as techniques for working around/maintaining contact with the line. Have to cut the line? There's techniques for that, as well as techniques for rejoining the cut line.
Getting confused in the cave and going the wrong way, going deeper inside the cave instead of heading out? There's techniques for that.
Gas? You only use 1/3 going in, max. That gives 1/3 to get out, 1/3rd in reserve, and your buddy also has that same reserve. If the cave gets more complicated such as it siphons heavily (meaning the current is sucking in, making it harder to get out), you may only use 1/6th going in, giving you the vast majority of your gas to get out. In some caves, divers will sometimes place an extra stage bottle (an extra scuba tank) attached to the line prior to a particular section of a cave where you could have more trouble than regular if you were to have cascading problems.
Someone panicking and taking the regulator out of your mouth? We literally set up our gear expecting that to occur. No big deal.
The portrayed death in the film would have never happened with proper cave gear due to the redundancy of our systems, and when wearing doubles the presence of an isolation valve...not to mention the ability to easily reach the valves to begin with unlike typical "recreational" gear. Unlike recreational divers that commonly drag their shit loosly, routinely tearing the shit out of reefs in tropical paradises...a cave diver's gear is much more well secured and streamlined, preventing such incidents from occurring.
Silt outs? Yeah, it happens, but when people don't have the emotional control it usually shows during the final exercise in cave class where your instructor takes you off the line, completely lights out, and you have to find your way back to the line. There's specific techniques for that which work.
It's really not the adrenaline rush extreme activity that people think it is. It's really quite relaxing. The vast majority of deaths come from people who are not trained cave divers, which is one of the points they tried to make in the movie. Military divers usually possess the self-control and in-water confidence to become successful cave divers, but they're taught zero of the TTPs for cave diving and do not possess the proper gear which is almost entirely different from the ground up. When someone who is a certified cave diver dies in a cave, it's almost always 1) They broke the rules to "push" more than they should have, or 2) Their creator decided it was time to punch their ticket, and they had a medical emergency while underwater.