There's already one, or perhaps two, aircraft launching when Shamrock requests a 15 mile departure leg. The controller has to immediately figure out where to place Shamrock while the other departures, including behind Shamrock, keep turning left. Shamrock has to go somewhere and it's probably much easier to keep Shamrock circling overhead JFK while the controller sorts out the puzzle he's been given. Behind the scenes were JFK east departures shut down as the controller needed to create another gap to fit Shamrock into as Shamrock's gap went unused? So stop departures until the aircraft that launched behind Shamrock, and then Shamrock, are straightened out?
Had a similar event years ago. After departure requested a slight right turn. Parallel departures off our right. Needed slightly more to the right. Knew that the controller hated it but we needed it. TCAS and radar and the guy ahead of us is heading into the garbage. Controller (stressed) - "everyone's taken the turn. The guy ahead of you is in the turn." We're surprised that the preceding aircraft took the turn. It's VMC and the weather is visible to the naked eye.....and then the radio springs to life as the preceding aircraft calls (strained voice) "we need an immediate right turn!!" The controller wasn't irritated at us anymore.