I not so sure that legally you even need a list of passengers. You should really know how many you have for weight and balance and that any baggage on board belongs to those who are flying (with appropriate exceptions). But common sense says once should be a available somewhere and a copy on board can be useful. But I certainly won't wait for a printed or electronic copy if it means a delay.
PM
ps. Missing passengers, paper PIL? Why not cross out the names of the misssing PAX.