There is a saying that the FARs are written in blood, as in regulations aren't passed willy-nilly, but passed after there has been a serious incident.
Air traffic is one place where "Iterate quickly and break shit" doesn't work. What happens when in the name of "efficiency", one tower reduces current safety limits because "99% of the time these are unnecessary", then the one time it actually was necessary, you've got two jets about to make a head-on collision, or one quickly changes course, loses control, and crash-lands into a town.
There are absolutely improvments that can be made with the FAA, but privatizing ATC is definitely not one of them.