I would be more comfortable with separating these two ideas:

  1. If NYC wants to bailout MTA and fund capital projects - they should pay from general budget/taxes/fares directly
  2. if NYC wants to reduce driving - they should introduce CP indepedendently of MTA's capital improvements plan, and don't tie these revenues to MTA at all. 

Start from a small charge like $1, then hike to $5, then $10, then $15 and observe change in motorist behavior and congestion observed.

Does anyone actually knows what metrics are used for measure "congestion" and what are expected change in said metric? Its all hand waving and wishful thinking wrapped in earth hugging religion.

MTA would have weird incentives, like they can break down trains to CBD, and force people to take Uber/cab to get to work and trigger congestion pricing tolls and watch $$$ going directly to MTA, while they are slowly doing "maintenance and repairs".

MTA must NOT be financially incentivized to cause transportation collapse and make $mln every time public transit is broken, and people are using cars.

Arguably, the incentive should be the opposite (via fares). The better MTA's service is - more passengers and more Fare revenue they receive. This is how a normal healthy transportation agency would finance their capital investments.