I think that really depends on where you live. Here it is basically the other way around, you order, you drink, order some more, and before leaving you pay the bill, with the bartender keeping a tab of what you ordered (these days with a mobile POS). The only "regular" exception is when they're about to close the place, then they often ask you to pay on delivery.

Except the "our card reader is broken, we can only accept cash"-surprise, I can only remember three occasions this actually caused some hurdle for me in the past decade-and-a-half.