There's no free lunch. Really.
Saying a heat pump is an over-unity engine ignores why it works: It takes something from something else; i.e. it creates an externality. Ignoring those is a common error of over-unity believers.
Heat energy is the level of excitation of atoms. It generally stores on a per-atom basis not a per-gram basis. What's relevant there is that water is the densest thermal media known, because it has 3 fairly lightweight atoms in a small space. Raising 1kg of water 1 degree requires reducing a great deal more than 1kg of other stuff 1 degree. 1kg of air is a lot of air.
Also heat pumps aren't always one particular efficiency. Their efficiency varies based on conditions. For instance if you have 10C/50F pool water on a 35C/100F day, the heat pump is "pumping downhill" as I like to say, and it will be quite efficient there. Raising 20C pool water to 23C/75F on a 11C/52F day is a great deal harder and less efficient. The 6:1 efficiency you claim is only valid in certain test conditions.
"To keep the heat pump in its working range, I'm placing its condenser inside the utility room".
The heat pump will steal heat from the room and place it in the water. That gives you 2 choices, neither one good:
- allow it to chill the room, reducing the heat pump's efficiency badly, until it gets to 10C/50F, at which point the unit shuts off, or reaches 1.0 efficiency at which point it amounts to electrically heating the water "the hard way". Or
- divert additional heat into the utility room, which you then have to pay for. Now if your regular hot water heater is gas, and your house's furnace is gas, then it's six of one, half dozen of the other. Except you are paying the pumping costs also. So it's a net lose.
"I'll just eject the chilled air outside, then. SOLVED!"
Except when you push air out of your house, you draw a vacuum (negative millibar) inside your house, and air simply leaks in somewhere else. This "makeup air" now needs conditioning. Now you have 2 problems.
- You are "heating the great outdoors" by intaking -5C air and ejecting 10C air.
- The makeup air is much drier than the air that went into the heat pump. Here we must do a deep dive into latent heat of vaporization, but the upshot is that water vapor in the air stores a great deal of energy - 2,258 J/g or 1 megajoule per pound. When your process has the effect of reducing humidity, it's throwing away this latent energy, which must be made up for real. Effectively, "heating the great outdoors" and "humidifying the great outdoors" is the same thing.
Some of this latent energy goes into the water - the heat pump's evaporator (of freon) condenses water, and that 2,258 J/g went into the hot water, which at least isn't "humidifying the great outdoors", but still presents the same problems I discussed in the first part. Your humidifier must make up for this lost humidity, by boiling water into the air, again at 2,258 J/g. Even if it's a sparger humidifier (which sprays a fine mist which spontaneously evaporates, there's still no free lunch; that evaporation happened by stealing the 2,258 J/g out of the air, reducing its temperature and the heater must work harder to compensate.
If you want a heat pump water heater, just buy one.
They are readily available. However they solve none of the above problems. They're not the panacea one might make them out to be.
However... if the heat pumps could be water sourced.... (i.e. their interchange fluid is water instead of air)... different deal. Now you can pump water out of the aquifer and put the heated/cooled water back in (at a different height obviously, so you aren't trying to chill water you just chilled).
And if you're where I think you are, you have a second option, as long as you don't mind a house that is 7' or 13' wide (depending on if you're willing to limit yourself to broad canals). You can interchange to canal water (uptake from one end of the boat, discharge to the other). Or simply run a bunch of glycol loops before you pour floor insulation, and use the boat's entire steel bottom as your heatsink, without ever having to clean a clogged filter! Covering an entire boat roof and upper sides with walkable solar panels has not been done. So much opportunity for innovation!
Placing the heat pump on the intake line to the water heater is a lost cause. Water only moves through that pipe while hot water is being used. (cold water pushes out the hot water, that's how the pressurization works; the volume of actual water in the tank remains the same). Doing that would be like having a "tankless on-demand heat-pump water heater" and that would require a positively enormous freon engine and evaporator, we're talking 20,000 joules/second (aka watts).
Having the heat pump recirculate through the water heater (out the drain valve, in the cold) won't work either, because its maximum temp is below the water heater's minimum temp.
"It will work at night when the water heater gets super cold" Actually, any competent, modern tanked water heater will hold usable temperature for at least 12 hours after power loss; and if it doesn't because it's old, they make rockwool insulation kits for them. Of course, hot water won't be replaced as it's used, but yeah, you can get a shower before the system turns the heat back on.
"Storing water around 100F, what could possibly go wrong?" Actually it'll breed all sorts of bacteria, including legionella. (you may not have heard this because it's relatively new science, partly arising from the fiasco in Flint, Michigan. Tiny amounts of bacteria were in water pipes because of a botched water-supply changeover [from the regional lake-water system shared by most suburbs, to obsolete plant drawing from the Flint River]. That, plus the "petri dish" effects of water heaters kept at 40-55C, created a perfect storm.)