I'm assuming you believe that the telephone and airplanes were developed
by the government, or with government help. So, go and prove those two points.
Also, the government must've invented the automobile, and computers, according to you. Oh, by the way, how much money did the government contribute to creating one of the most, if not the most important inventions of the last few centuries, namely, the typewriter. Oh, and how much money did the government contribute to Ben Franklin, when he decided to go experiment with kites and electricity.
No doubt that, government assistance for research and science can help make new discoveries and usher in new innovations/projects, but, most of what science and research is about, comes out of the innovative spirit and incentives which people already have. People might need help to conduct research on certain ideas, but first came the idea, which means that, government came second.
Space research had been done way before government got involved, and, the U.S. only became heavily involved in it, after the Soviet Union beat the U.S. to space while putting a satellite into orbit. At that point, we had no choice but to take the pooling of resources, which is what government really is about, in order to try to overtake the Soviet Union. Lacking that motive to go into space, we probably would still have gone into space, but at a slower pace.
Government can partake in R&D, but, it's participation is overrated, and, in many cases, unneeded, and, oftentimes, intrusive.
