Could New York build a new mega airport?
I think I'd challenge your assumption of insufficient air traffic capacity.  You could equally well look at it as too many planes wanting to land, or (for NYC at least) insufficient passenger rail service.

Beyond that, have you looked at land prices in the vicinity of NYC or London?  Perhaps in some countries you can just seize land to build airports, over the objections of the people living there.  In the US (and presumably the UK, though I'm not certain), it's much more difficult to obtain, and should properly involve paying a fair market price - after long and expensive legal battles.

Then you have to consider trip duration.  It's not just time spent flying, but time getting to and from the airport.  In NYC, it's IIRC about a 15 minute bus ride from LaGuardia to Manhattan, and I think not much more from JFK.  Put the airport way out in the country, and people would spend an hour or two just getting there, negating the speed advantage of air travel for short &amp; medium length flights.