This isn't about a time with no worries in their respective present, this is about the future. A couple decades ago there still was genuine hope for the future, an almost certain expectation that the future will be better.

A look at science fiction will confirm that: You get none of the space utopias from the sixties that honestly believed in the goodness of people today. There is only bleak techno dystopia from the nineties onwards, where everybody fends for themselves and no hope for long lasting peace is in sight.

If we all try reaaalllly hard, we might get there at some point in the future. Until then it's a nice fantasy.

14,000,000,000 BCE

I don't think there were many existential threats before MAD

Personal existence has always been threatened since we had the ability to understand mortality, the new stuff (MAD and climate change) are pretty unique in that they threaten civilisation as a whole, and that's pretty new