My plane ticket receipt contains fees for half a dozen various government costs, including airport fees and a general US transportation tax. The FAA is pretty trivial, having a budget of just under $10B out of total American spending on domestic air travel of more than $800B.
https://www.transportation.gov/sites/dot.gov/files/docs/miss...
https://www.statista.com/statistics/207075/domestic-travel-s...
For all I know air travel may very well be subsidized, but you'll need to point to some serious numbers for it to be anything like the money that Amtrak hemorrhages as a fraction of its revenue.
That program is around $3.35BB of the $10BB total FAA expense.
Essential Air Service subsidies Airlines serving rural communities which significantly increases overall ridership. Air Transportation Safety and Stabilization Act as just one example was 10 billion in loan subsidies after 9/11. Another example most Airports are heavily subsidies at least during construction, but so is some airline infrastructure like Indianapolis handing over $300 million for a United Repair shop. The military intentionally creates a huge stream of trained pilots without costing the Airlines a dime.
All of this is intentional so no one subsidy seem all that large, and adding up a thousand little pieces take enough effort that nobody complains.
PS: "Per passenger EAS subsidy in the 48 contiguous states plus Puerto Rico ranged from $10 to more than $977 per passenger in 2014" but it's only ~300 million per year so no big deal right. https://en.wikipedia.org/wiki/Essential_Air_Service
Just a thought, but if you're interested in numbers, it's an eye-opener to look at how much money airlines have lost for shareholders, bondholders, and the government via bankruptcies. If passenger rail was ever capable of tearing chunks out of the economy the way the airlines are, it must have been a century ago.
From 2011: "The industry in aggregate has lost about $60 billion over the 32 years since deregulation"
https://www.npr.org/sections/money/2011/12/16/143765367/why-...
I'm pretty sure airlines are one of those unusual industries in the US (like banking) that have throughout their existence lost more money than they've ever actually generated in profit and have been kept whole by the government. Sorry I don't have any hard figures on that.