The 'half' figure is mostly primary vs final energy accounting. A heat pump delivers 3-4 kWh of heat per kWh of electricity (COP 300-400%), and an EV turns ~80-90% of stored energy into motion vs ~25-35% for an ICE drivetrain. So electrifying heat and transport shrinks final energy demand even before counting upstream losses (refining, thermal generation - roughly 60% rejected energy in most Sankey diagrams of the current system).

The comment below about electricity prices is the real friction point though. Where time-of-use rates exist, running a heat pump with thermal pre-heating during cheap midday solar hours changes the math entirely - the building itself becomes the battery. I got into tracking my own load against TOU windows and ended up building a small tool for it (energy-iq.app); shifting ~40% of consumption off-peak ended up worth more than any single efficiency upgrade. Electrification halves the energy; rate-aware scheduling is what makes it halve the bill.