One thing that some cities have done where awkward infrastructure is required to get a train to the airport is to, essentially, borrow money to do it, and make the fares to the airport very high to compensate.
Notably, getting to Brussels airport, which takes about 15 minutes from Brussels Nord, costs about 15 euro. For a 15 minute train journey. Hands-down the most expensive train per minute (or per km) I've ever been on. But, at least in theory, it's paying for this thing: https://en.wikipedia.org/wiki/Diabolo_project
(That's by no means the only one; lots of airports are in awkward places so running rail to them is expensive, and it's common for it to be paid for by special, more expensive services. And people use them.)
Yep, Stockholm's Arlanda express train is costly as well
Even at 15 Euros I bet its way cheaper than a helicopter or electric VTOL aircraft
Oh, yeah, and it can and does handle a scale of traffic that a helicopter service obviously couldn't. I think each train takes about a thousand people and they're every ten minutes or something.
The "use helicopters for airport access" thing seems, at best, extremely niche.
Joby plans to expand way beyond airport access, it’s meant to be basically flying rideshare. The key enabler is they designed it to be quiet enough to not annoy everyone around like a helicopter, so that it would be reasonable to have this thing taking off from residential neighborhoods. JFK access is just a very visible first test run.