You don't need to build an airport, you rent space in existing airports.
Renting in the main city airports is very expensive but the ones further out aren't so bad.
Renting in the main city airports is very expensive but the ones further out aren't so bad.
To organically grow, you'd need to find desirable and under served routes between smallish airports, build a loyal following, then maybe you take a risk, borrow money and attempt to move mainstream. Not impossible but it seems like you'd need just tons of money.
Is there much room for value add and innovation? The most obvious area I can think of off the top of my head would be an airline that did all their own security and skipped tsa but I don't know if that's allowed and I think the work would be akin to building your own airports.