I think it makes sense to combine a heat pump with solar collector, furnace flue, clothes dryer, waste water and other available heat sources. I've seen almost no mention of this possibility. With a heat pump we can produce an integrated household system, storing heat more efficiently, distributing it directly to both space and water heaters, reversing it for summer cooling.
A solar collector, which is often hotter than its surroundings, loses some of its heat. One with heat pump coils would be kept a little above freezing, much colder than most collectors, making it more efficient and reducing necessary size. At least in warmer climates, low collector temperatures would make glazing unnecessary, even counter-productive. Without glazing, even on cloudy days, a heat pump can still collect heat from ambient air. Also, in summer, such a collector could dissipate heat for cooling. In areas with frequent below freezing but sunny days, some form of removable glazing might be worthwhile. The collector would include some thermal mass to reduce off/on cycling. More and more, instead of a roof being seen as only for the purpose of keeping the elements out, it's also to bring the sun's energy in, efficiently.
There are also hidden advantages to installing heat pump coils in a furnace flue or stovepipe. (First we must be able to produce a very clean-burning firebox and use stainless steel or other corrosion resistant flue materials.) Fuel burning stoves lose considerable heat in the form of water vapor. Water is an unusual chemical in that 1. it has a high "specific heat", (a lot calories of heat must be transferred for a given amount to lose or gain in temperature), 2. it has a high "heat of evaporation or condensation" (takes a lot of calories to change it between liquid and gas) as well as a high "heat of fusion" - (freezing and thawing). We can recover the heat of evaporation, and the "sensible heat" (proportional to temperature change), by cooling the flue gasses sufficiently to condense the water, and then some. Ideally then, we are left with cold water and dissolved chemicals (which are drained off), nitrogen and carbon dioxide gasses, and a little excess of oxygen to insure clean burning. Hopefully, condensing water would wash away any solid smoke particles in the flue. Removing the water from the gas makes it lighter and easier to move on out. (I have lots of other ideas about wood stoves, which unfortunately aren't on-line yet. I wrote them before I had a computer.)
The heat of evaporation is also a factor in connecting the heat pump to the output of the clothes dryer.
One might also want to run the heat pump, blowers, lights etc. off a gas generator, which would furnish yet another source of heat, connecting both the compressor and generator to the engine by electrically controlled clutches.
Such a system would be complicated (even without a generator), ideally with many computer-controlled expansion valves. But I think it will happen eventually, and it's not beyond our abilities today.