A flow of 2 litres per minute from a hot tap is woefully inadequate, and while some people might think that's acceptable, most will not.
Let me preface this by agreeing with you that an all-electric (give or take whatever fuel is used to generate the electricity!) UK is pure science fiction, at least for the next many decades, if not more. I have just been responding to the specifics of what you said.
As I've been implying, it seems to me that this is all about filling baths. Unless you're thinking of something I haven't considered, I can't think of anything else (other than filling baths) for which 2-3 litres/minute (or whatever) out of a hot tap wouldn't be adequate. As for baths, as I've said, no matter what form of fuel one uses, I can't help but wonder whether they aren't an energy-hogging 'luxury', the wisdom of which we perhaps should be seriously thinking about.
Likewise anyone who currently has a stored water system delivering 15-20 litres/minute for a shower isn't going to want to change to a pitiful 10.5kW electric effort supplying less than 5 litres/minute.
Maybe not, but if one went with your other suggestion ["a stored system where the water is heated over a long period of several hours (as in immersion heater / cylinder)" ] they wouldn't need to. That's precisely what I've been doing successfully for the past 30+ years - a 3kW immersion heating water in an extremely well-lagged cylinder for 7 hours every day(night)** - but, again, the 140 litre cylinder (and hence the amount of 'slow heating') would be inadequate if we wanted baths.
[ ** I would add that, in terms of energy (rather than power or current), although 'powered' for 7 hours per night, my immersion consumes an average of only about 5.5 kWh per day ]
P.S. I do have a second 140 L cyclinder and immersion, but that it virtually never used - other than usually for a day or three if/when we have 'a full house' at Christmas!
Kind Regards, John