The mains are shared with your neighbours, so a hot water main would also be shared with neighbours. So just like running the hot water in the bathroom sink before a shower means hot water gets to the shower quicker, with hot water mains, your neighbour having a hot shower before you means you'll see hot water sooner.

Though my country does not have hot water mains. I wouldn't be surprised if the heat losses are enough that even sharing a water heater between unattached neighbours is less efficient than both using their own heaters, let alone a whole city doing that. Though maybe tropical areas could do it.