> Stepping “in the arena” with odds like those, I’d say the vast, vast majority will back out and/or break down sobbing if forced.

Something like 10 million people will accept those odds. Let's say 1 million are healthy enough to actually go to space and operate the machinery. Then let's say 99% will back out during the process. That's still 10,000 people to choose from, more than enough for NASA's needs.