NYC issues medallions for yellow cabs in order to limit their number, in part , to avoid congestion on the streets. Picture an Uber driver who's from queens having to take a ride to Brooklyn or the Bronx and they don't really know the neighborhood at all (not uncommon). They have to pick up their fare, get the person to wherever they want to go, and then try to navigate the trip. Then they need to navigate their way out of the neighborhood, usually gumming up the locals in the process.
As of January, this year rideshare cars outnumber yellow cabs 4:1. I know they're not all on the road at the same time, but even at half capacity there are 3 times as many cabs on the road as usual. You notice the difference pretty easily. This comes on the heels of the TLC giving out a bunch more medallions to a few thousand "green" cabs (not yellow cabs) which are intended to operate in the outer boroughs and north of midtown only.
https://ny.curbed.com/2017/1/17/14296892/yellow-taxi-nyc-uber-lyft-via-numbers
MTA subway ridership numbers have not increased at all in the past three years, after rising nearly every year prior to that. People are taking individual rides instead of getting on the bus or going down into the subways. Traffic was bad enough before rideshare car services proliferated. Now it is worse.
Edit: Uber works great in the suburbs and in cities that could use more capacity. It works well in NYC, too because people get to where they want to go at a reasonable rate, but it does reduce the quality of life in NYC.