For example, could you successfully take and read a temperature, give the correct medication dose, clean and dress a wound, clean up vomit and remake beds, remember to check on them regularly if taken ill, etc.
At the more dramatic end of the scale could you get your kids out of a burning house, see to a choking child, take a pulse, accurately explain their condition to 111, decide when it's time to throw in the towel and call an ambulance, arrange for someone to care for any other kids while you go to hospital, etc.
To be honest I’d have to be pretty wasted to have problems doing any of those things. I wouldn’t drive if I’d had even a single glass of wine, but I could do everything else after a night out, yes. Not pass-out drunk, but I don’t think anyone is advocating that.
I think people are talking about two different things here - is it ok to allow even a sip of alcohol to pass your lips whilst in charge of children - yes probably. Is it ok to be falling down drunk, slurring your words and throwing up in the toy box? Nope, both because you can’t make safe decisions, and your children will find it scary if they witness it.
I don’t think most adults get that drunk on a regular basis though - I certainly don’t, and the only people I know who do are actual alcoholics.