If people are willing to accept an increased risk of dying for a dollar value, that means they don't value their life infinitely. If they did, no amount of money would be worth an overall increased chance of dying.
What is a good approximation for infinity value for an 18 y.o. with a high school diploma?
If they were perfectly rational, it would be the present value of all expected future earnings.
Such a calculation would make taking a job as an oil platform underwater welder make sense.
Trouble is, it is only a convenient approximation. It can expand to fit any circumstance.
So if you own, say, a trading company worth $10 billion and you hire someone (or some entity) to be in charge of protecting your life, the substrate on which all of that value rests for you, you've just handed them a check for $9 billion plus the present value of all of your expected future earnings and asked them to keep good care of it.
How do you think a perfectly rational actor would respond?
That is demonstrably false. Everyone of us could, at a cost, reduce his chance of dying tomorrow.