{{{{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.