Just to burden the discussion with a few facts (darn, not a PPRUNE tradition but ...)
Funding for the US FAA is appropriated by Congress ...all of it, every cent, regardless of where it comes from. There are two major sources of funds (1) airport and airways development trust fund and (2) general revenues (what the IRS vulture collects from everybody).
ALL the capital costs in the Facilities and Equipment and Airport Improvement appropriations come from the trust fund which all comes from taxes and fees on aviation. For the Operations appropriation it is about 70 percent trust fund and the rest general revenues, it's different each year. The philosophy on this is that the military and other public use aircraft compose about 20 percent of so of the aircraft operations and they don't pay any taxes so that proportion of the cost of running everything should come from the general revenues, not the trust fund. There are also functions that the FAA does that are functions of soverignty like international relations, spectrum management and just existing and other misc. stuff that a country should do anyway so the general revenues should pay. The research and development appropriation is a pitiful $100M or so a year, a little more than the total of the navigation fees collected, a relative drop in the bucket.
The notion that if direct fees were introduced then GA would not use services that maybe they should (IFR and ATC services in marginal weather, for example) has been around awhile. It seems a logical argument but I have never seen it proven. Would be interesting to see what has happened in other countries.
It seems that there may be a chance of privitizing some services and functions, but what has been going on for years is the "stealth privitization by parts" by contracting out engineering, services, support and other functions while keeping the in-house capability small, weak, and tied to things that no company wants to do.