I don't think of it as a right or a privilege. I look at it as an honor and a fantastic learning experience that shouldn't be abused. As such, if you are going to ORD or JFK, you need to have the skills to fly a fast approach and the ability to handle the radio and taxi. And do NOT go at rush hour.
Say hello to the bad guy because I went to JFK, LGA and TEB with Bob. (Whatever happened to that guy?) We went in the middle of the day when it was quiet. No holds, no delaying vectors, no long traffic jam, just in and out. Same at LGA. I had no interest in going to EWR 'cause...well...it sucks. At the time I was a very low time pilot and it was an awesome learning experience.
I have flown something like 2,000,000 miles on commercial airlines, which I think equates to about 6,000 hours as self loading freight, mostly in and out of NYC. I have literally spent days of my life waiting for a gate or in the congo line for departure at JFK or LGA. No bug smasher has any business going in these airports at peak times or with weather delays but when you are not taxing the system, no harm no foul. I don't know what happened that caused one or two planes to go around but obviously something went very wrong on this flight.
And yes, it's pretty selfish to delay passengers if that really happened but commercial airlines have cost me and every other good customer they have many thousands of dollars due to incompetence, timed out crews, maintenance, needless delays. lost luggage etc so the fact that a piston single cost Delta a go around, god bless him. If anyone missed a connection because of a go around, the airline had already screwed up and was way behind schedule.