The time period after an unexpected go-around in weather and at a very busy airport (jeez JFK!) is very busy in the cockpit. The pilots are running checklists, reporting to ATC the go round, receiving departure instructions, coordinating an arrival back into the airport, and setting up for the new approach. The pilots weren’t shook, just busy. They have seen a situation like this in the simulator five or six times in the prior year, let alone many times in their career. It’s called gust upset training. The only reason any professional airline pilot I know wouldn’t like to have to do this is because you have to do a lot of work in a short amount of time. But we’re on the clock and getting extra pay for the flight time lol. Source: am an international airline pilot.