IDK about you, but in temperate middle Europe if you don't heat your house at least some when it's empty, Oct-Apr, you are going to spend way more to get it at 19-20°C when you come back. Not to mention the pipes risk exploding if you let it go close 0°.
That's incorrect. It will always cost more to maintain a temperature while away than to heat/cool when you aren't. The area under the curve of temperature difference vs. energy use is what you're optimizing for, and that curve has a higher slope when the temperature difference is high.
It's not that simple. If all of society turns all of it's home heating to max at 5pm to prepare for a 6pm arrival, we'll need to overinvest in either generating capacity or storage.
Not to mention the fact that houses aren't completely empty when the adults aren't there. Kids, pets, plants, and last but not least, pipes with water in them. All of these will die horribly in cold temperatures.
