Doesn't mean it isn't done. Hospitals do it in Phoenix. But it's cheaper to just turn up the nearby nuclear plant.
On-demand systems (gas and electric) are available, but I've not personally been in a house where they were used for other than quality of life (i.e., providing hot water sooner than and until the water can get from the hot water heater).
At least, in my experience this is how it goes as a homeowner.
So to get to an on-demand water heater you'll probably have a lot of electrical work that needs to be done(potentially thousands of dollars).
What really bothers me is that you always read that they are instant.
The fact that they are instant is not because they don't have storage, it is because they are smaller and thus could be placed much closer to where you need the heat. The problem is that everybody who replaces their hot-water tank puts that 'instant' (I prefer the term on-demand) water heater in that place.
The following is anecdotal, I promise you, I'm not lying, but again, N=1.
We have one that we unlocked to go up to 140F (default 120F for protection).
I live in North Phoenix, bordering the desert, so it gets to around 32F (8 hard freezes last winter).
The capacity of our hot water heater, which is already high, as they really work hard, isn't enough to heat up city water fast enough to get water that is the temperature I like, in winter. Remember that thing needs to heat up water from say 40F to 140F. And while it can do that, it cannot do it at the same pressure as the previous one with a tank. It'll literally reduce pressure if it cannot reach the right temperature, which is really annoying, as that makes the overall temperature go down.
The previous one with the tank was 140F, got refilled with 40F, but could deliver me a much more continuous pressure for much longer.
Some have, some don't. Heat pump is just a vapor compression cycle with a reversing valve. Having water/dry air/moist air/air with water mist/ground/sewage as a heat source or sink is a matter of design and application.
From a marketing perspective it’s not (as far as I’ve seen) driven by eco credentials, but by not needing planning permission - external AC compressors are not automatically permitted in the UK.
[0] https://www.urbancooling.com/water-cooled-air-conditioning
Water is actually expensive.