Most major cities I've been to have a train to the airport that is not part of the regular subway system. That requires a different type of ticket, etc.

This is especially because airports are frequently further out from a city than the subway system goes -- you need light rail.

But the A train is a subway that actually connects directly to the AirTrain which goes around the terminals at JFK.

So I don't think it's a reasonable complaint that you have to connect to an AirTrain that goes around the terminals, or that getting to Newark requires NJ Transit instead of MTA. This is entirely normal.

Also, the subway is not "the main" transit mode. For a huge proprotion of people in the metropolitan area, they rely just as much on NJ Transit, PATH, LIRR, and even Metro-North.

LaGuardia is honestly the only one that's annoying, because the connecting bus is more annoying.