If you put 10000 really smart people to the task of solving big problems while giving them nearly unlimited resources, they could get a lot done.
Of course that's not how entrepreneurial funding actually works. For better or for worse it takes a really unique financier (like the government) to make that happen. The moon landing was the product of a really unique time in our history, I wish we'd stop using it as an example I guess.
But why was it unique? Why couldn't it be duplicated? Why shouldn't it?
The only difference is between that and the cold war is that people don't give them due attention because they are non-anthropomorphic (a fight with nature instead of against other humans). If it was the soviets who were behind the asteroid threat, and they were causing old age and cancer, and they were behind worldwide poverty, the US government would be mobilizing trillions of dollars to tackle those problems.