it sounds like that may be part of the problem, it is in some sort of limbo. it is not private and it is not directly under the city, as such the city does not take full responsibility for it and you end up with a mess like this and nobody really stepping up to the plate (from the city).
Personally, i would trust the city running it (I believe Bloomberg wants to). They do a rather good job with sanitation, with parks, with emergency services, etc. and i would think they could be trusted with the transit as well. it would make sense as we have all seen now how integral mass transit is to the city.
At the same time, i always am in favor of privatization and competition as those often result in improved efficiency and quality - but of course this contains some risk as the city is not in full control.
perhaps privatization with strong regulation may make sense (similar to yellow taxis? where there are also private car service to compete, but at the same time they are regulated enough to make sure they serve the public properly)