I agree with you completely. My country has an out-of-control safety culture that has many unintended effects. For example we are one of only a handful of countries on earth with a cycling helmet law. As a result, fewer people cycle and drivers take less care around cyclists. Lots of studies have shown that at a population level it's quite possible helmet laws have a negative impact on health and safety. I am currently travelling Japan and I have seen thousands of cyclists and not a single helmet (and very little in the way of dedicated cycling infrastructure). To my knowledge Japan doesn't have an epidemic of head injuries.
Safety first doesn't mean "don't do anything unsafe," it has a broad meaning. With your interpretation I suppose it could mean if you're going to do something, be sure to consider your safety tradeoffs first.
I think “safety first” generally means that you should put safety first when you’re doing something but that I should consider the safety trade offs first when I’m doing something.
No it shouldn’t.
Safety is almost always a trade off of real (or perceived) risk and reward.
If safety came first, you’d never swim, hike, or drive a car.