Oh, heat pumps do work. Of course they need lots of electricity, especially in the winter. And they cost around 20,000 Euros for a (very) small house, you rather need two.
But since energy comes out of the wall plugs for free there is nothing to worry about. This may be even true if they engage some nuclear power plants to provide the energy, but with solar panels alone? No nuclear energy, no coal, no oil, no gas? In the winter?