1) That would make the previous 3rd generation before this current iteration (one cycle ago) the generation that experienced WW1 - they'd hardly be ignorant of the horrors of world war.
2) Boomers (your 2nd generation) went through Vietnam and the cold war, so I'm not sure they often felt like the UN was safeguarding them from, well, anything.
3) Boomers also seem to be indifferent and apathetic about climate change, so I'm not sure how that really fits into the narrative.
The most likely answer is that most people just feel indifferent about things that feel out of their control. Boomers likely didn't spend every waking minute about how close they were at several points to being ended by thermonuclear war.
Hell, even for the greatest generation (well, except for Murrow obviously) let McCarthy run rampant right after WW2 until he tried to go after the army.