Those are the exceptions to the rule. How many planes and routes do you need to even merit consideration at a major airport?
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.