Not a controller, but did visit the TRACON asking a bunch of questions:

ILS 13L very rarely used. While you're on the base (heading 030-060) you're going up the East River and they have to keep you at 2800 to assure terrain clearance with the WTC (1750 height).

Once they turn you on an intercept heading (090 and clockwise), you are heading AWAY from the obstacles and they're able to give you lower.

Traffic is NOT a factor since only JFK traffic will be in the sector. They wouldn't have IFR traffic passing underneath you -- that's for sure. The nearest IFR traffic would be LGA arrivals going up the Hudson at 4000.

If the controller says Telex at or above 2100 (it's really 1800 I believe), then s/he doesn't care what you do altitude-wise as long as you don't 1) Climb, or 2) cross Telex below the altitude specified.

My $0.02.