Can New Yorkers make ballot propositions? If so it might make sense to make the MTA responsible directly to voters who live in the counties that are served by MTA. The current situation where it exists halfway between the governor and mayor seems like a governance structure where everyone can just blame the other person, similar to the governance structure dysfunction plaguing Washington, D.C.'s metro.

And part of the dysfunction of the DC metro is the lack of dedicated funding.

Accountability and power need to stay in the same hands. Being held accountable for a task you are powerless to affect is a powerful recipe for dysfunction. In context, funding is power - the power to make decisions about who gets how much funding and resources to improve the system. If you have funding, but no accountability, then you will simply redirect that funding to projects which are are actually accountable for.

Electing an MTA head, without giving that head dedicated funding, will be a political nightmare.