{{{{That makes no sense to me. It fires up and instantly starts heating the water. All the heat goes into the water and into the dishwasher, except for the heat in the water left in the pipes at the end when the use stops. The latter happens exactly the same with a tank type unit. Nor do some of the other comments here make sense:}}}}
They make a lot of sense if you look at how a demand WH works.
Take a pot, fill it with cold water and put it on the stove. Turn the burners on high. Then dump out the warm water and refill with cold water. Repeat that scenario over and over again. That's exactly what's happening when you use a demand WH for to fill a dishwasher. It takes a fair amount of heat to bring the heater exchanger tubes up to proper temp. You basically keep reheating the pan. You never get to take full advantage of the "warm up" energy. In addition, the burners in many demand WHs are rated for a 2.5gallon/minute flow rate. But most dishwashers don't fill at the rate of 2.5 gallons/minute. If the dishwasher fills at the rate of 1 gallon per minute, all those extra btu's go right up the flu. You can do the math on this yourself. The worst part is that the dishwasher refills several times in a cleaning cycle. A shower, on the other hand, provides maximum efficiency because it's using the proper flow rate for the BTU input. The downside, of course, is that if your demand heater is rated at 2.5 gallon/minute and a second person tries to take a shower, the demand heater can't provide enough hot water. If you size the demand heater to 5 gallons/minute, then you're wasting even more fuel in low volume operations.
I wasn't saying that demand heaters aren't efficient. I was just pointing out that they're not efficient across the board. If you use them at the rated flow rate, they're far more efficient than most tank models.