Many electric pressure washers have this system, usually called a total-stop system.
However- electric pumps require cool water running through them so they don't overheat. Most owner's manuals allow no more than 5 minutes of idle time with the pump on, but no water running through it, or damage will result.
The only pump we carry that can be run dry for hours with no damage are the pumps made by Kranzle and found in their pressure washers.