Heat pump electric hot water heaters, good or bad idea?
Water heaters are generally the biggest energy drain in a home after heating. so Air-to-water heat pump water heaters are potentially a big energy saver, particularly when the main heat source in a home is an air source heat pump, as the water heater can in effect 'borrow' the efficiency of that heat pump, which on average is about 3 times more efficient than most other heat sources. See here for an article on how heat pumps work.
An air-to-water heat pump water heater uses the air in the house to generate hot water, so the more efficient the air heating system is, the more efficient the hot water heater will be. That's why you get the most out of it when you pair it with an air source heat pump, because they are a very efficient heat source when combined.
Heat pump water heaters are less beneficial in homes that heat with gas, oil or electric resistance heat since there really isn't much of an energy savings in winter, however in such a case the water heater can still help with summer air conditioning as it removes heat from the air to generate hot water and produces cooler air for in the home. Where there is hot humid air, which is usually the bathrooms, a heat pump water heater can recyle this air, drying it and removing the heat in one operation while heating hot water for the next bath or shower, so we think they're a good idea overall, but you may also want to consider tankless on demand hot water heaters for which there's a guide here.