Many busy supermarkets in SF default to a single line. Trader Joe’s on Market, and Whole Foods on 4th do this. I’ve also seen it at Whole Foods in Manhattan, with reader boards to tell you which check out to go to. Works great!
The reader boards work like a circular buffer. If you pay attention to where the pointer is, you may even jump ahead a few spots by entering the right queue.
Depends on the implementation. In Poland, in all the stores I've seen employing single queue for multiple registers, the board is controlled by cashiers - there's a button at the register that the cashier can press when they're ready for the next customer, and the board always displays the number of the register that signaled readiness most recently.
