It costs less to run because less energy is used; I'm pretty sure incandescent bulbs aren't emitting anything by themself!
"The push" is from the government, perhaps consumer demand is "the pull".
A counter example is a water pump, which converts electricity into gravitational potential energy of the water as it flows upwards.
My point was about efficiency of the generation. You want the light, you don't necessarily want the heat.
Save heating for the (efficient) heat pump.