Privatization is the very definition of "Penny wise, pound foolish," for the many sectors. In the end, it costs 3 times more after all of the oversight (DCAA, etc.). Privatization is definitely not cost effective in the defense world. The same will be true of ATC. Someobdy is going to still have to oversee it, and that basically means you will be nearly doubling the number of jobs that need to be paid.
First, you are going to use a company whose sole purpose is to make money. This can happen three ways. 1) Make processes/employees more efficient. 2) Pay employees less. 3) Charge government more.
Idealists / ignorants like to think that #1 happens, but it mostly doesn't. #2 and 3 are what happens.
Next, the government will still oversee everything. This includes a shitload of people to make sure that the contractor that they hired is charging them appropriately for EVERYTHING. That's not even getting into safety regs, investigations, etc. which will still be done by the gov., or independent private third parties, also charging the government. Next, you're going to have jurisdiction problems. Who oversees what? This normally ends up in 1) Territorial inter-agency disputes. 2) The creation of a new, intermediary "go between" to resolve those problems.
In short, privatization of many things is totally ass backwards.