Agreed ... but in order for the US to push through their rocket program, they needed scientists and researchers to develop, test, build, test, retest, and test some more all of the applied science that had been developed. The country needed to build an entire community of thousands of professionally trained technicians, scientists, engineers, professionals ... and with them had to come teams of administrators, academics, trainers, bureaucrats, office workers ... and with all of them had to come entire groups of trained builders, workers, electricians, plumbers, draftsmen, planners and all the people that came with ... and all that had to be supported by an industry that needed to build and develop all the things that had to be needed to get this monolith moving, which meant that all these corporations and businesses needed their own teams of professionally trained people.
It was a massive investment in education in order to get the ball rolling in industry to build the rocket program. It wasn't just building rockets ... it was building an entire industry upon industry upon industry to get to the point of building a single rocket that could launch anything into orbit.
The reason why any of it happened was that the government heavily invested in educating and training an entire population to make it all possible.