They will simply slow-walk the process. It already takes 2-6 months in small rural upstate/western NY counties....and that was pre ‘the summer of mostly peaceful protests’....
I’ve heard from friends it’s always been 6-months plus on Long Island, I imagine even longer for NYC. So all this means is that unlike before, after the 4,5,6,7+ month process they can’t turn you down.
But all they need to do is have a single bureaucrat processing ALL applications and it’ll take over a year....
Around the Capital District it can be fairly quick - Rensselear County, a bit slower in Saratoga County, and like molasses in Albany and Schenectady Counties. In Saratoga County they require a permit for 1 year and then a shooting and classroom course. I like the course if voluntary, but it's mandatory.