Preliminary but important point: what you call prevention is typically called 'mitigation' by the UNFCCC, NASA, and other environmental orgs, while what you have called mitigation is typically 'adaptation' [1]. I know this is jargon, but if you have conversations with folks in the environmental/climate field it can in the best case provide instant rapport to at least be speaking the same language, and in the worst case, at least prevent serious mis-understandings.
>>The other thing is that people don't really think this is a true emergency. An evidence for this is the quote "What if global warming is wrong and we made the planet better?" If it is a true emergency, we should be doing stuff that make the planet worse if it is wrong. We should be pushing nuclear power - even to the the point of reducing existing safety regulations. A Chernobyl every decade is preferable to global warming. Politically, we should be willing to trade existing environmental regulation for those which reduce CO2.
-Human perception of danger/emergency has, from the evolutionary perspective, been optimized for concrete, near-term events/entities, eg terrorism, explosions, enemies. On the other hand ,it has not prepared us for preparing against abstract, medium to long term adversaries, eg planetary or physics scale changes that threaten civilization, malevolent ETs, malevolent super-intelligences [AIs].. etc etc.
-Even if this weren't true and we didn't have these unfortunate cognitive bias, your argument about broad public wisdom of emergency relies upon a well-informed populace that is familiar with statistics, and the scientific methods. Unfortunately, that is not the case in almost every advanced Representative state on the planet. This broad ignorance renders the ambient public awarness point you have made quite moot.
-Finally, I see the logic behind the 'what if global warming is wrong and the planet gets better' case as analogical to Pascal's wager, or the false postive; what you forgot to mention is the false negative, which is metaphorically relatively similar to the outcome of Pascals (Hell/Earth becomes like Hell).
[1] https://climate.nasa.gov/solutions/adaptation-mitigation/