Though I haven't seen the full data on privatization, I would agree that for something like national infrastructure, it's not the best idea.
The best way to "fix" ATC would be the same thing that should happen with other long term infrastructure sections of the government - the budgeting process needs to be reworked. A lot.
I saw it in things like our satellite programs. While you could get a satellite in orbit (often with a one time budget plus up), you then had to fight every year to actually run the program, and the budget could fluctuate more widely than the Iranian stock market. That's basically a waste of a satellite, because you run into times where it's just floating around doing nothing because there is no money to analyze and use its data.
It does no good to say that ATC needs to be modernized, or even do it, if after it's done, the FAA has to fight congress (both sides of the aisle) every single year to keep the modern infrastructure running. There needs to be a budget exception for important infrastructure like this that guarantees a minimum baseline funding that not only gets the equipment installed, but keeps it all running at a "level" level. Something like a 5-10 year budget that doesn't fall under annual congressional squabbles, or for that matter, the foibles of the American voter.