Ok, the part that might make this YTA for me is the fact that whenever he stays up late (for video games or otherwise) my husband is CRANKY the next day. Less tolerant of simple childish mistakes, suddenly a bit shouty, etc...

OP if you are even mildly irritable the day after, then YTA because your slightly unpleasant mood affects the lives of everyone you live with. Kids especially take parental crankiness very hard. Suddenly normal behavior gets snapped at. Things they always do are too much. It leads to inconsistent parenting which makes kids insecure and anxious because they don't know if they're getting normal Dad or tired Dad.

So, OP, If you wake up and are all sweetness and light, and don't sleep till noon while to wife watches the kids, then NTA. Buuuuuuuut party of me thinks this isn't the case.