I forget where I saw it, but I think the 14th street closure allows local deliveries. Trucks find it easier to deliver because they no longer have to double park.
Not sure what the actual statistics would be, but using Google streetview, it seems that trucks/vans are maybe 20% of traffic. Taxis, limos, Uber, etc. probably make up another 30%.
Private autos are probably on the order of half. It would be interesting to know what percentages are trips NJ to LI/outer boroughs, LI/outer boroughs to Manhattan, and NJ to Manhattan.
I personally would not drive in Manhattan unless absolutely necessary (not for decades!) and have only crossed it in the dead of night or from the GWB to the Bronx.