The NYC subway purse strings are controlled by the state.

You kind of just proved the point.

NYC has a majority power over the state purse strings and Albany has the majority of what's left.

If you want a mountain of money for the subway all you need to do is earmark it at the bottom of a repeal of NY-SAFE (or whatever you call that gun law that the rest of the state hates).

I'm ok with this. I'm also lazy. If you write a letter to our state assembly I'll co-sign it.

So they can get things done, but not without help from nation states?

exact opposite. NYC subway is in disarray partly because it is controlled by the state and the state political interests are not the same as the cities. The city effectively funds the state as NYC pays more in taxes than it takes out. Not true for upstate.