Pot luck works the same way. Whatever anyone brings is put out for everyone. Beer is brought in coolers but are set out for everyone. So you wouldn’t be breaking any rules by grabbing a beer out of the closest cooler. Some people only drink one kind and that’s what they bring and what they drink, others don’t care so drink whatever. It’s not all in one cooler (most of us don’t have coolers quite that big) but it is for everyone. At the end of the party or cook out, everyone takes their cooler home and whatever is in it.
Bring wine, it’s chilled in the cooler or fridge and offered to everyone. Rarely any left to take home and most would only possibly grab unopened bottles they brought and usually after asking the host if they want it.
Keep in mind, everyone here stays at least to the clean up stage. Everyone pitches in with the clean up and putting away of leftovers. During the process, everyone is asked if they want to take any of this or that and it’s divided up.
So Suzy brought one dessert and Lisa brought another. Suzy May take home some of Lisa’s dessert and some of her own and visa versa. Or it may be divided up betweeen several people.
Cook outs, craw fish boils and the like may include 50-100 people. Everyone brings at least one dish, sometimes more and everyone brings beer, wine, drinks or a jug of tea. No one wants to keep all that.
And here, a tin of cookies or a bag of chips may not get opened as there is so much home cooked stuff. And the person who brought them is always just expected to take them. They bought them and they weren’t touched. Why would they be expected to leave them? Pot luck doesn’t usually include “hostess gifts”.