This article was trying to make the claim that at many birthday parties in the US, all the childrens' parents will stay at the party. I don't know how common that is, but some cursory searching does indicate that it's a thing.
Drink coffee and try to socialise with other (equally agonised) parents because you somehow have to manage to spend two hours together until the party is over?
That sounds about the most horrible way to spend your time, to the point where I'd eventually consider not taking my kid to these parties in the first place.
If you want to stay (and are wanted) that speaks to a strong sense of community which is nice
Chat with other parents—but then my kids are young enough that the parties we go to are still mostly for kids of my friends.