the prerequisite for fast electrification is cheap electricity. Currently many EU countries have expensive electricity for households

This is just objectively untrue. Source: I live in Germany, a country with some of the highest electricity prices, I drive a BEV and I heat my home with a heatpump. My systems SCOP hovers around 3.5, which means that my kWh of heat made from my heatpump with electricity is cheaper than my current gas rate.

My heatpump electricty bill is significantly lower as compared to my apartment (Gas furnace), despite both buildings being roughly comparable late 80s construction.

I charge my car at my standard electrcity rate of 32ct/kWh, and I pay now about half for the same usage.

Electricity is expensive, yeah. But electrified stuff is also significantly more efficient than fossil tech