> We can extract a lot more energy from fossil fuels in large scale plants

This isn't true at all for natural gas. Burning it for heat in the home is much more efficient than burning it in a plant, converting it to electricity, transferring that electricity, then turning that electricity into heat.

In addition the sibling comments (COP of heat pumps is 500%), air pollution in homes is worse than air pollution outside. If you don't have natural gas and burning fuel, it helps a lot. Not only is electricity cheaper and cleaner, but also healthier.

Depends, if you are turning that electricity into heat using a heat-pump you might win on most situations (maybe lose if the weather is really cold outside, unless you add geothermal loops, but then its a lot more expensive to make)

The theoretical efficiency maximum for burning gas in a home is 100%. Most systems won't hit that because they need to vent waste gases, which carry some heat away.

Heat pumps are significantly more efficient than 100%. They can get to 500% efficiency. So no, it's definitely not more efficient to burn gas in a home. (To say nothing of the safety of running gas lines to every house.)

That is false. Heat pumps are more efficient than burning gas in a home even when the electricity came from burning gas.

But isn't it more advantageous to have the gas -> electricity conversion in a plant from an emissions point of view? You still have losses in the system when moving natural gas around from the source to individual homes too (leaks). In theory you don't, but in practice you do.