the government even subsidises people who are willing to invest into converting their houses into "low energy houses". Why would they do that if it was useless and would even consume more?
The government did not pass the Law of Conservation of Energy and is not in a position to repeal it
All I'm saying is, if upgrading your insulation, eliminating draughts, installing a heat-pump, and leaving your heating on all the time produces a "low energy house" -- then upgrading your insulation, eliminating draughts, installing a heat-pump, and
not leaving your heating on all the time will produce an even
lower-energy house.
The only way it might be otherwise, is if the heating system itself is more efficient at low outputs than high outputs. This is, to a certain extent, the case with heat-pump systems (it certainly isn't with conventional fossil-fuel or electric heating), but even so, if the reheating after a cool-down is gradual enough, it still seems likely to be a win.
Peter