ATC is there to provide specific services that increase safety and throughput (mostly by sequencing and separation).
If you did this with the ruling class, they'd likely pass regulations that would benefit themselves disproportionately and hurt general aviation (the small little Cessnas flying around). There is already a bunch of problems with privatized ATC, don't make it worse.
But yes, it inevitably devolves into that in practice. Because money gives you more time to make your voice heard, or delegate it to someone else representing you. Or simply bribing others.
The ruling class flies private aircraft and don't have to operate out of large municipal airports.
I don't think it matters much to them whether they spend the hour in traffic out of JFK, or on a highway from White Plains.
Depends where you're going though. DCA looks pretty convenient if you're visiting the capital; but lots of big cities have smaller airports that are more convenient if you can land at any airport.