But if you use that gas furnace to heat radiators in a fluid-born (usually water) heating system, you only need to install an electric heater next to your furnace and re-route the pipes to/from the furnace to use that heater in stead. Not all that humongous an operation.

Green hydrogen derivatives would make that theoretically possible. This is receiving quite a lot of attention in the EU at the moment. In practice, the stress is more on industrial processes and other primary energy use scenarios.