Seth, what makes you think someone who can afford and wants to get there by air tansit is going to want to end up on public transit? Also aviatoreb made a great point. How can people trust the service unless you can guarantee 7 day a week service, no excuses? When it comes to making it to work, it's better to be stuck in traffic but know you'll end up getting there than to arrive to the airport to learn the plane is broke down or weather isn't flyable.
Insanely rich people can do this by helicopter. Then they really are saving time because they go departure to destination and pretty much direct. If you gotta drive to an airport, wait for all the other passengers to arrive and be loaded, fly, then walk to public tansit, then wait for it, then take it... what the heck?
As I'm sure you know by flying angel flight, it's different when it's volunteer based. You have no problem to refuse, cancel, postpone or do whatever to the flight as you're not being paid to do it. It's strictly voluntary and I think a component that makes it safer. When you start putting things on a schedule with small planes, you're adding a lot of risk.
I'd be glad if you could pull it off, albeit surprised, but I don't see how it could be made reliable and quick enough to justify it. Now a $50 helicopter service from DC center to NYC heliports would be interesting