"OTOH, no private company has been able to produce one, from launch pads to mission control center to landing area, rocket testing, assembling, satellite integration.
It requires a big number of steps to get something into space (lots of factories depending on each other to be ready on time), with the authorizations."

Boeing builds airplanes, but doesn't operate airplanes. America Airlines, doesn't make planes, nor does it operate airports, but is one of many airlines. But the private sector does move millions people through the air.
Boeing's Space branch builds rockets, it also has Sea launch operations, it also builds satellites.
The private sector is unlikely to operate as NASA operates, and it probably wouldn't because it very poor way to conduct business. The private sector has competition, it's forced to do things efficently.
There is *no good* reason why NASA *needs* to be an operator of space vehicles.
Going to the Moon was the source of this wrong headed approach- the private sector was not in the position to go to the Moon- and to go to the Moon to wave a few flags within a basically "unrealistic time frame" was even more unlikely. So NASA was capable of taking huge amounts of tax payer funds and directing it at a project of going to the Moon. Then stop going to the Moon, then destroy 100's millions of dollars worth infrastructure to make the Saturn V.
Amazing, perhaps- useful, practical, reasonable, and/or economical definitely not- unless, you are in a war of ideas with country that wishes to enslave humankind, then it's very reasonable and economical.

It's quite possible that if the Soviet Union hadn't been a threat and the US had not gone to the Moon with Apollo. By this late date in time, that the private sector would had gone to the Moon and would be merrily mining water and is colonizing Mars. Now, it's also possible that the Soviet threat was a source of moviation- an without it we might still be flying prop planes. It's hard to know because what it all depends on is what is wanted by people AND how this is affects governmental direction which then has "feedback" on the public [maybe- or maybe "something" else is going on].