In this case, having to pull workers out at inconveniently short intervals to keep doses down is a specific nuclear nuisance (heavy construction/demolition work, plus aggressive dust control, isn't any faster because the workers are limited to very, very short shifts); but I was thinking of the much broader, and much older, cultural habit of putting certain people (mostly those who needed a very particular combination of independence and motivation-management) into a role where they are The Leader, and enjoy nontrivial power; but if things go bad, they have nontrivial responsibility, and it is both considered shameful(and often illegal) not to fulfil that as well. Take ship captains. That one in Italy is being raked over the coals right now over the question of whether or not he left his post before all possible rescuing was done. That's not because one pudgy 40-something was considered vital to the rescue effort; but because he was The Captain, and being the captain means that that is among your duties. Some military designations and higher level government posts(where resignation is effectively mandatory on the occasion of certain types of scandal, even if you could easily mount a legally sound defense) carry similar flavors.
As for the 'nontrivial power' bit, there are certain people who you want to put the fear of god into and make, within their sphere, more powerful than people who would ordinarily be above them on the hierarchy. You want the captain to be able to say "Listen, the nautical something system is not seaworthy. There is no way that that ship is going anywhere under my command until that is fixed. Period." You would want a nuclear plant operator to be able to say the same thing about the system under his charge. Those are just the sort of functions where you need to power, even impunity, some of the time(do you want the guy handling safety systems to know that he'll be fired if he raises any expensive questions? You would want him to be able to barge into the CEO's office and tell him that This Isn't Bloody Good Enough, if that's what it takes. On the other hand, you can't just toss him a load of general-purpose power and impunity; because failure to carry out his own assignment dutifully and correctly could have very, very, messy consequences indeed.