My family does this! We call the game Demon, the piles “demon piles”, and we shout “demon” to end a round. The rules are the same as you described them, except possibly that we allow “stacking” multiple cards to place them on the same common pile simultaneously; this follows the same rules as placing them sequentially, except that (naturally) nobody else can interrupt. (I can remember a time when we played without this rule, so it may be a house rule.)