O'Hare is a huge international airport, which provides services that rail can't touch.
I'm referring to smaller regional airports, which I guarantee don't cost billions.
ORD is the third busiest airport in the world with 60 million passengers per year.
Compare that to a system that will cost 3 times as much and will be lucky to get a third as many people through its doors.
Last estimate I saw about 5 years ago was that to add a runway to TUL was going to cost between $750M and $1B.
A "small regional" airport that could support commercial air travel still consumes at least 3 to 4 square miles. How much do you think it would cost to buy up 4 square miles of land in LA, San Fran, San Diego and every other city that will have a station along this train route? How are you going to convince the airlines to add capacity to all these routes, since many regional routes are money pits, meant as feeders for the mainline carrier, and if the airline adds regional routes between two regional airports, there is no feeding to the mainline routes.
So again, I don't think you can really just "plop" airports anywhere you want forever. At some point the current airports will reach capacity (look at the capacity caps at several airports already) and the airport will need to be expanded or a new one built, with buy in from the airlines, both options are very expensive.