Flow-through hot water heaters have been very common in European houses. They presumably save space, energy, or both. (They may be losing favor as Europeans get richer.)
What I hate about them is that it can be very difficult to adjust the temperature since it is dependent on the flow. If you are in the shower and the water pressure changes or you adjust the flow, the temperature changes. Perhaps newer or more expensive models don’t have this problem.
Another thing you see in European houses (or at least used to) is little (e.g., 4 liter) hot water units mounted above sinks. That’s another way to get instant hot water (albeit in small quantities).
When I worked drafting plans for naval ship architecture, we did a lot of piping systems design. Most of the ships had hot water recirculation systems, with a loop or two per deck. The recirc systems pipes were more expensive, but this was outweighed by non having as many water heaters and not having to run the showers for a minute before any hot water arrived.
For isolated spaces (rooms), just cold water was piped to them, and a little “instant” water heater was used.
And for further economy, water drained from sinks was sometimes filtered and used in the flush (toilet) systems. I don’t recall if shower-drained water was similarly recycled.
The Canadians. They walk among us. William Shatner. Michael J. Fox. Monty Hall. Mike Meyers. Alex Trebek. All of them Canadians. All of them here.
I agree that older flow-through water heaters had unstable temperatures. Very difficult to take a shower with one of those - have to keep adjusting the temperature. But newer ones are usually microprocessor-controlled and keep the specified temperature very well. My parents in Japan have a 10-year old system and I can take a shower there a comfortably as in any U.S. home.
However, I’m sure they are much more complex than the American tank system. I’d guess that it hasn’t caught on in the US for the usual reasons: the old system has always worked reasonably well, and the savings in energy and space is not enough to justify the cost and the fact that it’s ‘different’.