https://www.gps.gov/systems/gps/modernization/sa/
You can find a list of good reasons why they should never want to do this, but one of the big ones is that if they ever actually did they could only do it once, because then no one would trust them not to anymore and would start including hardware support for the alternative systems in case it isn't available.
But that isn't really the point. The relevant issue is that the US taxpayer pays for GPS and then the people of Italy and Australia and Brazil get it for free. Even if GPS had been an exception with some strategic defense purpose, how does that explain e.g. funding for cancer research?
I think this is a really cynical take. A government opens up a service that's benefitted billions for 50 years and you think it's so the US gets them "hooked"? They use it because it gives them value, and they (we) didn't have to pay for that value at all.
Do you think the US would vote for or against the UN to making a global competitor?