"Your factual claim that infrastructure would not exist without the government". Your desire to reduce this to black and white statements tells me you're only interested in convincing yourself you're right. "private telephone companies (dial up) would never have bothered wiring huge swaths of this country where houses or farms are miles apart." It's not too hard to deduce from my statement that private telephone companies would have wired parts of the country where homes were very close together and they could therefore reasonably price their services and capture a profit. And roads would be built to the most populous towns and cities where there would be enough traffic to create tolls low enough that people would adopt the roads.

Again, government investment in infrastructure makes a lot of sense, and happens, when the economics do not make sense for a private company.

  spending that the private sector would not take on... 
  The Internet would never...private telephone companies 
  (dial up) would never...SpaceX would not...only something 
  like a national government

Note your continual use of "only" and "never". You made this a black and white question. I'll freely admit that the government can build infrastructure; you should admit that history shows that independent individuals can as well. Then the question returns to the relative cost-efficiency of each provider, which was my original point. And that's an empirical question: could these services be rendered for less than $5.62 trillion in taxes per year?

The relevant question is not “could” they be rendered for less than $5.62 trillion, but “would” they be. From what I have observed, privatization of infrastructure does not typically result in cost savings; corporate profits soak up whatever was previously “government waste”.