Most of the uber price goes to the driver. So higher prices means more money for the driver. Since NYC is a more expensive place to live, and people have more money, you have to charge higher prices to get enough drivers to drive.
Make NYC as cheap as new mexico to live in, and you will see new mexico prices.
Because of the limit on taxi medallions, the market value of a medallion was as high as $1.2 million. When drivers lease the medallion it can cost $125 per 12 hour shift or about $85,000 per year -- an amount Uber drivers don't have to pay and thus should result in much lower fares.
Other US cities that are still expensive gave much lower fares.
Also there are many elderly on a fixed income that can't drive or negotiate mass transit easier.
Make NYC as cheap as new mexico to live in, and you will see new mexico prices.