What about electric water heaters? I am unfamiliar with the usage patterns and losses over time, but having my home water heater having some variability in temperature would be ok with me — I’d simply adjust the handle in the shower.
From what I heard they said something like a half-time for the heat in these devices of about 1 to 2 days.
And boost those with phase-change materials at the right thaw points.
* Too cold: Legionnaire's disease. Presumably not right away, so maybe there's some wiggle room if you're careful about timing.
* Too hot: scalding, particularly if you have kids. Maybe a new design could have a thermostatic valve on the output to give more flexibility.
There are also quite a few people who use thermal storage with wood fired boilers. The boilers burn the most efficient and cleanest when they are near full output, then hot water is stored in an insulated tank to intermittently supply the house with heat.
Description of one such system: https://www.newhorizoncorp.com/PDF/ekomanual.pdf