The excuse that the controller(s) were overworked/overloaded is wrong. Their job is to keep things safe....
Not sure they should be firing people when the ATC system is down in numbers, especially if they are long-term experienced controllers... unless they really have to in order to set an example.
A good friend is a former tower controller retired from ATC. First at JFK, then at a non-federal contracted Class D airport tower out in the country (cost of living in NY was too expensive for him).
He explains at JFK (probably all towers too) there are slow times throughout late night shifts that don't need the full compliment of day or evening shifts of tower controllers. Daytimes there are some ebbs and flows, but at push times safety demanded the most.
Bringing recently hired (some from the military) controllers into the tower can and do at times take up to (in his experience) 2 years before they are fully up to speed and trusted on their own, without another set of eyes watching over them. It was not uncommon at both types of towers to have new controllers cycled out and away to other less busy duties and locations. My friend believes that busy towers are the most demanding ATC job, with the highest level of collision potential.
A quick story recently relayed to him from a Class D tower friend about a new hire that was struggling during a busy time handling multiple arrivals, the last of which had just landed and sent over to the ground controller. Then, he sat down in a chair and said, "Whew, I need a break" and began scrolling on his iPhone. The supervisor said, "What are you sitting down for? There's five planes lined up who've been waiting to depart, get them out of here." I'm sure there are other similar stories, some related to understaffed ATC positions, and others for the caliber of some people hired and placed into the system.
On the job supervision of recent hires by more experienced controllers is likely to be in short supply at many facilities. Experienced long-term controllers are retiring out and taking their experience and skills with them. Don't know if this was a factor at LGA, or not.