[leoedin]

Every air-to-water heat pump install will have a hot water tank. So I'm not sure why "don't work well" is the term used.

It is true that heat pumps coefficient of performance drops as the output temperature increases. So you need a proportionally larger hot water tank to store the same amount of energy. So it is fair to say there are tradeoffs. But hot water storage is still a necessary part of most heat pump installs - because peak output of heat pumps tends to be below the heat demand of showers.

[coryrc]

EDIT: I misread "ripping out these energy storage devices" as https://en.wikipedia.org/wiki/Storage_heater which are basically bricks with nichrome wire.

You're right, of course heat pump water heaters use tanks to smooth out DHW demand, but that same thing isn't feasible for space heating.