Shorter RC constant allows deeper setback temperatures and thus lower average temperature#. This can only be improved by either decreasing the Cp*mass of the house, or by increasing available hating and cooling powers. Both require different paradigm in design where the standard is quite opposite: high Cp*mass, lowest heating power (heat pump) and lowest cooling power (good insulation). Does not make much sense to me but somehow this solution is preferred, over a short RC house, at least in colder part of Europe.
Short RC indeed improves controllability, but for a high cost: small R means high loss of energy. Insulation slows down adjustments but quite obviously reduces the consumption. While it prevents such tricks, it also makes them unnecessary. So if low RC comes with low R, it has no upsides.
Now if we choose large R (good insulation) which is obviously always a good thing, this still lets us to adjust C. Choosing as small C as possible would bring us some of the controllability, not as short RC as in a poorly insulated house, but still something. This allows the trick discussed here (savings by dynamically adjusting the indoor temperature according real needs). However, high value of C allows
different saving tricks:
* No need to switch between heating and cooling (or suffering overheating) when the
average (24h) outdoor temperature is close (or tad below) to desired indoor temperature. Low-capacity houses suffer from the fact you need to heat the house during night time and then at daytime, when sun is shining (even worse if windows are large), the house overheats (you lose the free energy by opening windows and ventilating) or even worse, you need to start cooling the house.
* You can heat/cool whenever the energy cost is lower; for example, with heatpumps, heat when the temperature difference is smaller, cut down heating power during coldest time. Or, follow the hourly energy SPOT prices. Or, follow your own solar production.
I think these "tricks" are WAY more valuable than the quick controllability of low-C houses.
This is clearly visible here, old-style massive brick houses here, those that survived WW2, are fine without heating or cooling from late spring, through summer, to early fall. They consume less energy in reality than on paper (when simply calculated from thermal resistance of materials, obtaining U value). Modern low-capacity well insulated houses require on/off heating and cooling around the whole year. They consume more in reality than on paper.
But you can have both if you want to: build with low-C materials but add a water storage tank (at least some 2000-3000 liters). Then you have the storage capacity but it's under separate control so you can choose when to charge, when to discharge it by adjusting valve positions.