You can go to JFK for $11.15 including taxes and fees from pretty much anywhere in NYC. LGA is even cheaper!

At a cost of about 2 hours of travel time, sure.

Not in my experience.

Quite often taking a car took longer for me, including finding my Uber or Lyft in a sea of others (great system, really, requiring everybody to find "theirs" when they're all pretty much doing the same thing!), navigating cancellations etc.

Of course, if you live far from public transit it's a different matter, but many people in NY do live close to a subway station.

FWIW google maps really overestimates AirTrain travel time, it was close to 1 hour door-to-door from my old apartment in LIC

The only time I was late to JFK was the one time I tried to get there by car and ended up on a ramp in Queens, completely stationary, for over 2 hours.