Your thinking on the dirty grid might be false. If you use a heat pump you typically get more heat energy than the energy you input. A heat pump can multiply the energy you put in by a factor of 2-5. Say you burn 1 unit of gas to heat your apartment. You could let your utility burn that liter and give you 50% of its energy in electricity (assuming half is lost). Then you power a hear pump which operates at COP of 2x. You get the same amount of heat as before. Now if the heat pump operates at a higher COP, you end up saving on burned gas. It's only worse if it operates at lower than COP or 2 under these conditions. Depending on the efficiency of the power generator and transmission, those numbers would balance differently. I don't think they'd be worse though. 50% is a really low number.

The reason this doesn't break the preservation of energy principle is that heat pumps move heat instead of converting electricity into heat energy. There's always heat in the air if the temperature is above absolute 0.