Heat pump water heaters are powered by externalities
A heat-pump water heater warms water by chilling the room the water heater is in. On a sweltering hot day, that helps air conditioning load somewhat. But the rest of the time, it is adding cold and draft to a house you are trying to heat. So you pay twice: to run the heat pump itself, and then to replace the heat stolen by the heat pump. If your heat source is electric resistive heat, this is wholly worse than a normal water heater.
Further, the heat pump water heater will perform poorly if it is in a closed space. It will turn that space into a refrigerator, and then run inefficiently because it can't pump heat that doesn't exist. Of course all that inefficient pumping makes heat, and it will have that heat, at least. Hard on the machine and no cheaper than resistive heating.
Tanked heaters need to be kept at 60C/140F for legionella
In recent years, it was discovered that the bacterium which causes Legionnaire's Disease, among others, can thrive and reproduce in a water heater that is too cool. Because of that, the gold-standard advice of health departments is to set the knob at 60C/140F.
Meanwhile, we have the plumbing safety people saying that 60C/140F is too hot, and can cause scalding. That is also true. The only way to not find yourself in a dilemma is to have thermostatic mixing valves at every human-accessed hot water outlet. This is provided by most joystick faucets, and almost any modern style shower valve.
This higher temperature requires more standby power 24x7.
Electric tankless requires really big service
In Europe, they have "electric showers" which are an electric tankless water heater built into the shower and serving only the shower. These are modestly sized, on the order of 20-25A at 230V. It would not be hard for such an electric shower to support the bathroom faucets as well (though, not at the same time). The upshot is that electric demands for a single point of use are not extreme.
However, the public expectation is that a tankless is a "simple unit drop-in" for a tanked heater: that it installs in the same location and simply works the same way - i.e. all outlets can use water at once at high flow rates, until it runs out, only now, it doesn't run out! This is the expectation. The high flow rate expectation creates a serious problem that can only be solved by an ostentatiously large tankless heater - Americans are fond of 18KW, 27KW or even 36KW units. A typical American electric service is 24KW or 48KW. And since the huge heater runs at max power when it runs, a truly staggering amount of electric service must be provisioned for this heater.
This works much better with "point-of-use" heaters such as that electric shower. Imagine a house with four 30A heaters: one in each bathroom, one kitchen, and one for the laundry room. This is not provisioned the same as a 120A heater -- this is provisioned on the assumption that they won't all be running at once. This greatly reduces the house's design load to within the realm of the reasonable.
Note that most on-demand water heaters are fuel or inefficient resistive units - I'm not aware of any "heat pump" on-demand heaters.