The private sector is not investing in public transit in NYC because
IT IS NOT ALLOWED TO, not because it wouldn't if it could.
There used to be a lot of private sector public transit in NYC. Today there is none. That was not an inevitability!
Many cities around the world have extensive private sector public transit. E.g., Buenos Aires has privately-run public transit buses with amazing coverage of the city and surroundings. NYC's bus system is garbage by comparison to Buenos Aires'. The difference is that NYC's bus system is run by the city, while Buenos Aires' is run by private companies.
(It's always interesting to see what parts of the economy get socialized in different countries/cities. The public transit system was the easiest part of the private sector to socialize in the U.S., so that's what got socialized early. Elsewhere (e.g., in the UK) it was trains, telcos, medicine, etc. This allows us to compare results. It's never pretty, what results from socialization.)
Public transit in the U.S., and in NYC in particular, was very much a private sector function way back when. It seems unbelievable today that the private sector could build subways, but why should it be unbelievable? $19B is a lot of money for NYC, but it's a pittance compared to the capitalization of Apple or Amazon, or Elon Musk's ventures -- if only the private sector could do it, it absolutely would build a better transit system.
But the lesson has been learned: if you build something that cannot be moved, you will be highly vulnerable to takeover by the state.
Recall that the Baltimore Colts left the city in a hurry right before the governor of Maryland signed a bill appropriating the team...
You can't take a subway system with you should the city decide they want to own it instead of you, and you'll never be compensated the true value of the system you built no matter what the applicable Constitution(s) says.
Even if the private sector were now invited to invest in NYC public transit, without an ironclad guarantee that they won't get taken to the cleaners later, why should they?
But the point stands: if they were allowed to and not threatened with eventual state takeover, the private sector bloody well would invest in public transit, and it would do a far, far superior job by comparison to the state. We know that the private sector has, does, and will invest in public transit when they are allowed to and in locations where they reasonably believe their property will not be taken by the state.
If you wonder why Buenos Aires doesn't have a private sector subway system, the answer is obvious: the capital investment required for that is so much higher than for a bus system, that a private owner would stand to lose a lot more from a state takeover of their subway line than of their bus line, therefore no sane investor would invest in Bs.As.' subways. The same applies to NYC, except that in NYC the private sector is not allowed to run buses either...
You seem to have accepted the liberal mantra that some massive projects can only be run by the state. This is very, very wrong. How much evidence do we need before you and everyone else figure this out? Why would one believe that SpaceX is viable as a private company but subways are not? Elon Musk absolutely does not think this way. Yes, yes, Musk sure likes public subsidies, but I don't believe they are necessary for his ventures, and would much prefer that he not rely on them in any case, but even with subsidies his model is far superior to the state running those ventures outright.