It also eliminates loss due to the friction between moving parts.

What if you live in a warm climate?

People in warm climates still have hot showers and need to dry their clothes on rainy days or at night. Or maybe they want to heat up their pool to use all year round. There's always a use for waste heat.

Then it isn't so much of a win. I guess adsorption chillers might work with it though.

heat water? Most people do make use of water heaters for showers and laundry.