So that the house cools down massively during ventilation lasting 5-10 minutes is nonsense. The air is exchanged, and it has a very low heat capacity. After all, it is a gas and the total mass is therefore low, ergo only a little heat is transferred outside. The majority of the heat is stored inside the house itself, in the walls, in the floor. That is why it is as warm again shortly after ventilation as it was before.
I have now looked up a few values for a rough calculation:
Air density approx. 1.2kg/m³
Specific heat capacity 1kJ/(kg*K) (at isobaric state change, i.e. pressure remains constant).
My house has, I believe, about 300m³ of enclosed space. So 360kg of air. So if I lower the temperature by 10K (10°C) during ventilation and exchange all the air, that is 3600kJ. And that is exactly 1kWh. Per ventilation, of course. And I ventilate twice a day.
These are extreme values. Only for the smallest part of the year is it so cold outside that I really reach the 10°C temperature difference. On average, one is certainly still below half of that.
The controlled residential ventilation is therefore probably rather a replacement for permanently "tilting the window open." And that is exactly how its advantages are described by the proponents.
One question, I don’t really have one: would the controlled residential ventilation possibly also dehumidify the air? In summer there are always days when the outside humidity is so high, and inside it is correspondingly high, so I would have concerns about the moisture in the long run. Only you can’t do much about that by ventilating.