Have you considered how much American innovation happened as a result of:
- Government programs, the huge military budget, and the once huge space budget (which can be argued was really an extension of the military budget). Can you say for certain that the Internet and would have come about in the U.S. first if it weren't for DARPA? The advancement of computers if it weren't for NASA?
- Non capitalist or profit seeking scientists (Many if not most of whom are funded by the government or philanthropies).
- Luck. The U.S. has an immense natural resources to population ratio, perhaps the highest. It has, at present, virtually limitless land. It doesn't have to worry much about its borders or invasion. Our one border "worry" is actually a benefit to exploitive capitalism: a super cheap black-market labor.
Since you mention "private property", do you realize it is entirely antithetical to free market principles? See https://news.ycombinator.com/item?id=9942313.
Since you mention Elon Musk, could he have achieved what he achieved without $4.9 billion in government subsidies? (http://www.latimes.com/business/la-fi-hy-musk-subsidies-2015...)
I could easily extend this list and make a more powerful argument, but I have work to do. The point I'm really making is to be objective about your analysis of what is behind American innovation and success.
We won't even get into things that we call innovation but have not made the world a better place.