It does quiet down eventually. There's no scheduled departures 22:55-5:45 and only a handful of arrivals 23:59-6:45.

However, arrivals stay pretty heavy right up until 23:59 even on schedule and if you've got a lot of delayed flights (not exactly uncommon at LGA) - you may still have a lot of departures going out in the 23:00 hour.

I would not be surprised to learn that they're staffed to an appropriate level for what the schedule says is supposed to be operating at that time, but a very inadequate level for what actually winds up operating at that time on many days.

Initial analysis suggests they were running about 75% of full capacity in flight ops in the 15min prior to the accident. I doubt they were staffed to 75% of the daytime peak.