I've no doubt that the studies you are referring to are correct, on a bell curve, with the conclusion centering on an average household. Those of you from big families know, nothing average applies to you. I wonder if the tankless would still be at a disadvantage for large consumptions of hot water during a short interval. Perhaps so. If an average household is 2.6 people, and we are considering a household of 8 people, we've really changed the game.
The house we have now has hot water heat with a tankless coil mounted in the boiler. The hot water is infinite. Efficiency is probably horrible, especially in the summer when the boiler wouldn't otherwise fire but, I wouldn't trade it. None of the hot water piping is insulated though so, the wait for hot water at an upstairs tap can be long, even know there is a storage tank. It occurs to me that having a small, on-demand, tankless for the bathroom sinks might save a lot of energy but, effiency and saving energy, as factors alone, are only of interest to the environmentalist. If saving money is the goal, then the savings due to increased efficiency must be weighed with installed cost and expected service life, as well as how long one expects to remain in that home. If you want to get fancy, you could throw in payback period and opportunity cost as well.
The option for the water heater timer is interesting. I know the utilities around here will offer a discount if you install one. I may not have been clear in my previous post about the programmable thermostat. I was referring to warmer air during the shower time. It works. People take cooler, shorter showers when it is 2-3 degrees warmer. No studies to reference, only anecdotal evidence.