Well, the airports in question don't always fit that mold. Midway really can't handle larger aircraft, hence O'Hare's growth. In the case of JFK, well LaGuardia is also cramped for space but is also heavily regulated in terms of what can be flown out of there. Same thing with National and Dulles.
It's a weird cycle with air service. A city needs a good business environment for airlines to come, and many businesses need a good air service environment to come in.
That being said, I think PVD has a good shot at international service, obviously never the size of Logan but I think there is potential for a discount international carrier to come to PVD. I think the train station is key in attracting more service.
Another thing to watch is Southwest. They've set up codeshares for Mexico and Canada. While it seems they want to get codeshares for the Caribbean and Hawaii first, Europe is still on the table. PVD is a possible spot to have international traffic transfer over. The runway plays a role though.