The earliest recorded use of the phrase 'American supper' dates back only to the 1920s. At that time, it meant a social function where guests brought food and drink with a view to auctioning/selling it to other guests, specifically to raise funds for a particular cause. In other words, the food could perhaps be taken away rather than consumed there, which is what I imagine happens at a 'potluck' meal.
As to why 'American', I guess the concept originated in the USA, where there is probably more of a tradition of organised events in communities...what with apple bees, quilting bees and so on in past times. (They are constantly having "town meetings" in The Simpsons, for example, even today.)