Someone who always cries "sheep" and keeps asserting genuine issues are "just the flu" or "Russia won't invade" is similarly problematic.

I think that's absolutely true when it comes to the media's treatment of past outbreaks, but that doesn't apply to the situation in Ukraine, it's the opposite. The mainstream did not take the threat of Russian aggression very seriously, even in Ukraine. Also the people pointing to the nuclear threat are urging calm, the opposite of your typical "boy who cried wolf" scenario.

Not pushing the break when you are driving directly into a wall at high velocity is not crying wolf, it is common sense.

It is only comparable to crying wolf if there is no wall or if you are going so slow that you could just calmy reduce the speed instead of alarming people — if you are actually in control of the vehicle. If you are not in a car, but on a huge ship the wall can be further out and the speed can be lower and suddenly crying wolf becomes a high paid job. Climate change is like a big oil tanker: if we want to stop in 30 years we need to hit the break now.

The nuclear crisis is different, because there is no clear defined path, but the risk of nuclear war is not zero.

Sorry but you're trying to correlate unrelated concepts here. It still holds true that humanity has never been more informed about events in almost real-time. Sure the media wants to make profit, but that doesnt change the fact that a nuclear power is blowing up civilians right next to mainland Europe right now.