You missed my short comment suggesting more reading: https://medium.com/@hak1010/capitalism-versus-socialism-9ece51b5ff29. This text addresses in extend the main errors in your reasoning.

It is not about what American want or have been doing. Starting at the beginning of the 20th century socialistic ideas have soaked minds of Americans. Wilson liked what Bismarck was doing in Germany. Interestingly, some of socialistic ideas Bismarck was not testing in the whole Germany, but only in the eastern part, in the occupied Polish territory.

The right approach is in going to the basics of human behavior. This is the strength of the Mises writings. Humans always go after their individual best interest, despite that most of them would deny it most of the times. Socialists build all their ideological concepts on an illusion that they can change the human nature. Hard core capitalists, writings of Ayn Rand is the classic example, build their ideological concepts on accepting the underlying egoism in human behavior. They look for a political structure which is the most moral for humans as we are not as socialists hope they can make us to be.

Growing up in Poland, then a socialistic country, on daily basis I observed the hypocrisy of socialism as a system. And, I see it now in the United States, in the degree as socialism is already implemented here.