>Are there any real examples of a government entity in the US competing with a private enterprise in which it genuinely would have been better for the government entity not to compete?
Probably everything the government touches outside of keeping the peace and helping businesses function. Government schools suck. Government insurance sucks. Law enforcement often leaves a lot to be desired. I think one could make an argument that we'd be better off with a toll road system too, but for the convenience and privacy of not having to pay tolls.
It's easier to argue for government management when a service involves practically monopolizing space, such as a road, or if the project is especially dangerous or expensive (such as utilities or the military). But the fundamental forces of competition are still beneficial even in huge and monolithic projects. Even in cases of projects commonly run by governments, the competition emerges as being between governments instead of being between companies.
>contractors complain when the military fixes their own gear, and this is asinine
I agree, it sucks. I am very pro-market but I think the government should lay down the law in these cases and say that it won't tolerate abusive prices and it demands all the technical data necessary for routine maintenance, if not the entire product.
>It could just be incompetence. I read the construction contract. If I were a contractor, I would not have agreed to the fixed price and the steep late completion penalties without charging two arms and a leg and quoting a very long timeframe.
If credible businesses are putting in lower bids and they get passed up for a stupidly expensive alternative, that reeks of corruption. But there could be requirements or assurances that we don't know about. That's up to you to find out if you are interested in that case.