This was an early start on the recent post Where Do We Draw The Line? I think I will keep it unfinished for that reason.
You can have errors in both directions here. You can feel safe when you really aren't. That's the intro to most horror movies, I believe, and also the excuse most drunk drivers give themselves. But even without those extremes there are a few weaknesses to following your feelings of safety. Human beings are pretty good at evaluating an observable, immediate situation - though we are slow to react to unusual occurrences, which is where training and awareness comes in. Remote, new, or long-running risks which occasionally erupt we are less good at.
Be can also feel in danger when we actually aren't, or when the danger is so small compared to the everyday risks we readily accept (driving figures prominently here). This can cause us to act in less-rational ways. I don't think it is good to say irrational, if it is a situation where there is a real danger, just overestimated. Also, different people have to weigh risks differently. If you are going to encounter only six people today, all of them known to you, then surprises are at a minimum. But if you are going to serve 1000 customers today, or if you are a controversial politician who is going to to be appearing in front of a large crowd, then risks of having someone shooting you, or bringing a disease into your range, or a drunk accosting you is something you have to consider, even if each individual you encounter is low-risk.
What is the feeling worth? "Why did you take out hamster insurance?" I guess just for the peace of mind. So we are willing to pay money for the feeling. We do it all the time, and no one considers it necessarily irrational. On the other hand we have the worries about safetyism, particularly among children, of increasing their anxiety (and thus almost automatically depression) by bringing up boogiemen that make them skittish. Most adults have stories of childhood fears conquered - "I was afraid of thunderstorms until I worked as..." "When I was little I thought that women in long dresses were witches in disguise..." But there is a real downside here. There are some diseases that are more likely to recur once they have been kindled, depression and anxiety are among them. You don't want to get those early, because even if you go on to laugh at whatever you used to be afraid of, you still have at least some susceptibility. This was picked up first in the 1990s, of Holocaust survivors and people who had seen terrible things in WWII but gone on to have productive, even cheerful lives showing a higher incidence of depression when they were elderly. Sometimes out of nowhere. So even if you "get over it," there is some residual risk, and we don't want to burden our descendants with that. Scaring the pants off children without good reason is bad for them. Heck, it might be bad for them to scare them even with good reason, just less bad than not exercising proper caution.
I think there is a distinction between amount of caution and risk and type of caution and risk, that boils down to the idea "Can you learn anything from this?"