I'm not sure it was a lesson learned per-se because the captain was merely doing his job as fundamentally defined.
A captain has ultimate responsibility for the aircraft.
However there is a side question in relation to your post...
When you say "declared an emergency" in your post, the more interesting question would be whether it was actually formally declared by the captain (i.e. "MAYDAY") or whether the captain was merely "working with" ATC at a lower level, maybe "PAN" or maybe just informal "prioritised".
If the captain DID declare "MAYDAY" earlier in the timeframe then yes, Kennedy would have a lot to answer for if they were spending excessive time vectoring around.
But if the captain did not formally declare and then came back later and started bossing Kennedy around, that would be a different set of questions, focused on the captain.