I've never been to NY, but in other (European) cities that I've lived in, the main issue with congestion are parked cars: commuters have to leave them wherever they can, including at corners where they block traffic a lot more. About half to two thirds of Paris drivable area are taken with parked cars (most streets are one-way three lanes with cars on both sides).

If car commuters use Uber, you relax that source of problem. Not sure how much Uber substitutes for car commuters, though.