Wood gasifier ... nice example. We can also generate electricity centrally from wood, just as gas or oil could be converted to electricity if necessary. That is exactly the point, electricity is universal.
Yes, electricity is universal and therefore it makes a lot of sense to switch to heat pumps in the long term. But, and that is the big problem, improvements to the electricity mix are much harder than they sound. Apart from hydropower, the non-fossil world is hardly capable of providing base load power on a large scale. And hydropower is exhausted in terms of geography and acceptance for flooded Alpine valleys. Wood on a large scale consumes far too much fuel. As far as CO2 is concerned, wood is also an illusion, since the CO2 is only fully reabsorbed after decades. Intensive forestry conflicts with environmental protection just as much as "bio" gas from the worst industrial agriculture. Biogas from crop residues is hardly scalable. Wind and solar are not controllable and above all, photovoltaics are subject to unfavorable seasonal fluctuations since little electricity is produced when demand is highest. Acceptance problems for 200-300m tall wind turbines, fields paved over with photovoltaics and high-voltage power lines running across Germany add to this. Tidal power plants and the like are still a long way from being ready for deployment.
All this ultimately means that expensive overcapacities have to be built, expensive power lines and expensive storage have to be maintained. The grid becomes complex through many small plants, at the same time we also incur inverse economies of scale. The world of non-fossil electricity generation is by far not as rosy as some politicians would like it to be.