Earlier quoted context omitted.
Your theoretical analysis misses an important physical fact: houses are able to exchange air with the outside world, not just heat. As you heat a normal room, it will expel air in order to maintain constant pressure, and similarly, as you allow a room to cool, outside air will enter again to keep the pressure constant. There was an article about this in the American Journal of Physics [1, 2] a couple years back, and…
...but the ideal structure is not supposed to exchange air with the outside particularly because of this. That is why windows and doors have seals on them. I'm no mechanical engineer, but I've worked with enough of them in my career to understand that their goal is usually keeping a structure tightly sealed when ingress/egress paths are closed (of course opening windows/doors is a choice of the occupant, which if you…
With regard to letting a house cool down at night, that's impossible. If you heat a quantity of air from 273 K to 300 K at constant volume, the pressure increases from 1 atm to 1.1 atm. That may not sound like much, but it's better expressed as a pressure differential of 10 kilonewtons per square meter, and the surface area of your house is such that it could severely damage the walls and blow the door open -- popping it like a balloon.
(The fundamental mathematical error made by those who minimize this effect is ignoring the surface area of the building)