Modern electric appliances are often more efficient than burning fossil fuels. For example, the electric motors in cars are just inherently a lot more efficient than gas motors, not to mention less mechanically complicated, quieter, etc. (One of the reasons that electric cars today already have the lowest lifetime cost of ownership.)

At Rewiring America they found that electrifying all American cars, heating/cooling, appliances, etc would save 40-50% over fossil fuel equivalents just because of the inherent efficiency of electric machinery. This makes the problem of decarbonization 40-50% easier.