One of the main reasons I went heat pump electric in my house (I could have paid less and stayed with tankless LP gas hot water) is I'm just not that comfortable with gas, especially living in an earthquake-prone country. Even if there aren't leaks it's terrible for indoors air quality, and a worry when you have young kids.

I was worried going from living with tankless to a tank that we would run out of water like we did in my parents house as a kid but so far it's just never been a problem. I think it helps that while the physical water capacity of our unit is 370 liters, the internal temperature is 80 C and it uses a thermostatic valve to blend the output, so the "hot water capacity" is more like 500 liters.

heat pumps just run something similar to a reverse Carnot cycle on their refrigerants and use a condenser coil to release the extra heat to the water. So for all practical purposes it heats the water inside the tank in a pretty similar fashion to how a normal electric water heater works, it just delivers it from a slightly different source and it isn't electric resistive.

So no, not possible. Theoretically you might be able to do it with a stupid enough system of coils and a very ridiculous amount of power, but it wouldn't be efficient or practical.

I'm still not sure why not possible. A tankless waterheater is just a regular water header with a tiny tank (pipes count as a tank...). I know electric tankless water heaters exists - they draw massive amounts of power (I considered one for my house, but it needs 4x 40 amp, 240 volt circuits - like most houses in the US I'm limited to 200 amps total and I suspect at times I'm using more than the remaining amount (not for long, but long enough to blow the main breaker)