I think that this is one of Delta's big challenges.

JFK is a natural for so many European routes because of the huge O&D market as well as simple geography (it's generally on the way to Europe from most of the country, while ATL is not).

But being able to feed connecting traffic to JFK is very problematic because of gate/terminal space as well as slot constraints during peak time.

One thing I wish Delta would try is a series of one-stop domestic connecting segments into JFK. For example, OKC-SDF-JFK, or LIT-PIT-JFK, or BHM-TYS-JFK, or BNA-DAY-JFK. Do a Southwest-style turn at the stops (ground time max 30 minutes) so that the time penalty of a one-stop is still far better than the time penalty of a connection at a hub. Doing this would allow one to market "direct" and or "nonstop" service to NYC from all of those markets, and it would allow efficient feed from all of those markets without crowding the skies with nonstop service from each of them (which is realistically not possible anyway due to slot and terminal constraints).

For years, Southwest has used the one- and two-stop direct flights effectively, but Delta (other than the old ATL-BHM-JAN-DFW route) rarely did. It would seem to me like a way to get around some of the constraints faced at JFK while providing decent feed to the international flight bank and avoiding problematic double connects at other hubs.