NYC does have these. Called commuter vans. I know of at least one that I used to take down to Wall Street from the Upper East side. It was great. Fast service and a fraction of the price of a cab.
There are also Taxi shares in NYC, which are similar, but hold less people (4). These are somewhat informal affairs and you have to know where to go / stand. But if you're going downtown anyway, why not split the fare with 4 strangers?
For me it's always been the benefits (medical insurance, bonding, etc) that makes freelancing hard, though maybe that's all changed now with Obamacare.
Do what makes you happy. There's only one go around.