Because Americans love pop-icons, prophets, and messiahs.
It all started (as memory has it) with John Lennon. It wasn't his fault (from the beginning) but by the time the seventies came, pop-stars and all sorts of celebrities were established as more-knowledgeable-than-anyone-else-on-the-planet when it comes to world events and its' conscience.
So now, speaking out on "whatever" is as compulsory to celebrities as it is to rock-stars faking "a good time" on stage and guitarists getting up close to each other for a phoney "Right on, brother! We're rockin!".
No it didn't. It started before the 70s.
If you were alive in the 60s you would have heard tons of anti war and anti LBJ songs and chants.
The most memorable chant was Hey Hey LBJ, how many kids did you kill today? And One, Two, Three, Four, We don't want your fuckin war.
If you turned on your radio you would have heard songs like For What It's Worth by The Buffalo Springfield with Steve Stills singing about how the government oppressed the war protesters.
It was recorded in 1966 and was on the radio in 1967:
The Beatles stared singing and speaking out against the war in their songs in the 60s too.
Then there's Bob Dylan who wrote and released many anti war and government songs in the 60s.
In fact there were tons of anti war and anti government songs in the 60s.
It didn't start in the 70s.