I don't think having multiple small airports is better than expanding existing large airports (sorry, NIMBY's!)

Airlines tend to operate a certain level of frequency (or more) to one airport, so having more airports means the total number of planes in the air increases. This adds further pressure on ATC. For example, in Southern California, you have flights going to LAX, SNA, ONT and BUR, and while those airports themselves aren't maxed out like ORD, the L.A. center is one of the busiest (I think L.A. is #2 and New York is #1).

While it's not cheap, it is easier to add runways to existing airports than to expand ATC. Basically, you condemn land, pave it, and install ILS, which has been done many times before. ATC, on the other hand, is being improved but only incrementally. There is no silver bullet with ATC, unless you're willing to cough up hundreds of billions of dollars for it. The FAA's massive improvement plans a few years ago were a total disaster. It's not like buying another PC for your office, where you plug it in and away you go.

Furthermore, if you look into the distant future, ATC will hit a capacity wall (there is only so much atmosphere), whereas the amount of land, while expensive, is practically limitless. One airplane needs a fraction of space on the ground than it does in the air.

Also, having multiple airports makes it more difficult to service them with rail transit. And you have more highway construction and congestion for an additional airport and so on.