MechEngr, are you conflating two separate things?
Probably like many agencies throughout the federal complex, FAA utilizes private contractors for functions with regard to which it would be a significant budgetary (and in many instances, management) burden to staff the function within the agency's own personnel. And, given the very-legacy legacy nature of the Notam system, it would make sense that FAA would not choose to have limited budget resources dedicated to staffing the software end of an old system - as opposed to hiring the expertise from a federal contractor.
But having specific functions staffed and performed by contractor personnel, under contract with the agency, is quite a different structure or arrangement than "privatizing" the entire ATC - NAS-management set of functions into a new, separate entity (which is a fair if also incomplete description of how Canada, among others, changed its structure).
Reasonable people can differ about whether proposals for carving out ATC and NAS-management and shifting these to a non-profit or otherwise non-governmental structure are wise, stupid, indeterminant, wonky, or irrelevant. But if the subject instead is not having what probably are tens of thousands federal contractor personnel doing software work across the entire interagency landscape continue in that role, whoa, that's a long and difficult carry. At altitude. With an over-limits pack weighing you down. On no rest. And your canteen just went down a crevice.