(This is all kind of beside the point that NY's transit problems are mostly due to localized cost absurdity, but...)
I don't disagree that it's hard to quantify the exact economic value, but you can't use a free market to solve coordination problems like public transit.
Coordination failure in stages:
1) A transit line that goes where you want, when you want for only a fraction of your trips means you need a second means of travel the rest of the time.
2) Having a second means of travel on hand (e.g. a car) means that you're less likely to use the transit line when it would work for you.
3) Lack of use of the transit line leads halted growth and reduced service.
4) Reduced service further drives users away
5) Evidence of failure causes a loss of investor/government support.
6) Transit line dies slowly to the extent that political inertia allows.
Or to put it another way, asking a transit line to pay to for itself is like saying "if human beings really wanted world peace they could have all just disarmed!", ignoring the fact that until everyone else is disarmed you'd be a fool to disarm yourself.
And if you succeed and build a critical-mass, sustainable system you've just swapped your market problem for a natural monopoly and have to use non-market techniques to deal with the monopoly service provider. (And now we're back to NY)