In that world, military would just contract with commercial providers and use commercial GPS, same way they already spend hundreds of billions of dollars on products and services provided by private companies.
I can't imagine how one would think that's better than the current situation. Military contracts with commercial providers are an absolute nightmare. Is this not what even libertarians denounce as "crony capitalism?"
Most of technology procurement that military does is through commercial providers. This means that if there is a nightmare project, it will most likely be a done with a commercial partner, because most projects are done with commercial partners. On the other hand, there are plenty military contracts with commercial businesses which aren’t nightmares. For example, US military has a contract with Samsung for mobile devices. It is most definitely not a nightmare.
Government buying from private businesses is no what “crony capitalism” means.