A solution that'll anger people but resolve the capacity issus, all flights with not a final destination in USA can only connect through Stewart airport.

Do they have a sterile transit area to support international transfers? I didn’t think any US airport had that and US requires transit visas and immigration clearance to transit

Airport is at full capacity -> route more pax through other airports.

A lot of people benefit from keeping JFK full. Airlines, pax wanting direct flights to other destinations etc.

Currently ~20% of New York passengers are connecting passengers, you could route them through other airports and free up capacity with much less disruption then making the New York local passengers have an extra connection on the way out.

That airport has one cafe. It's a nice little regional airport (I know they serve international destinations I've flow out of it to KEF, but it's very small). I'm not even sure how many planes land without a final US destination in the US? The passengers may be going on, but are the planes?