Not if you use a heat pump, no. Modern ones have very high efficiency (above 300% as they're not actually using energy to make heat, just to "move it around") and work even in very, very cold temperatures. But you don't install tens of millions all over a country in a matter of months - you quickly run into bottlenecks like production, distribution, certified installers, etc.

You're not likely to get 300% efficiency when it really matters, in colder climates. The temperature outside my house is around -10C now, and closer to -20C at night this week. Keeping my house warm requires around 6-10KW constantly atm, which I could perhaps reduce to 5-8KW with a heat pump (some heating will come from other appliances, like computers, fridges, etc).

Or I have used the oil boiler in the basement, if Norway didn't ban that in 2020. That would have freed up enough electricity for several homes in the UK or Germany.

Electrical heating is fine if all electricity produced is from hydro, nuclear or wind/solar, but it makes less sense if the grid relies too much on fossil fuels.

Depends. Better to burn gas for direct heat than burn gas to produce electricity and then use resistive heating.

But you do have to transport the gas or electricity to the heating site, and I don't know how that adds up.

Also, if conditions are right, you can use electricity to run a heat pump and move heat from the outside air to the inside air; depending on the details, you can move a lot more watts of heat then you spend operating the heat pump. This can be more economical than direct heating.

In a sense, but if the worry is carbon and energy security then domestic renewables and nuclear look a lot more attractive.

Heat pumps are great and super cool but if you include the efficiency of generation it's unlikely to be more energetically efficient, yes.

It's close though, natural gas combined cycle plants are very efficient for what they are. And if the heater is electric, substitution for other electricity sources is possible... unlike now.

It is, but why would we want to burn gas and invest in gas infrastructure instead of carbon free technology? Electric heating works great for any future technology we end up using.