I’ve recently had a Zip InLine CEXU instantaneous electric water heater installed in a workshop building where it doesn’t make sense to pre-heat and store hot water. I’m only ever feeding that with cold but the manual makes it clear it’s happy with a variable inlet water temperature anything up to 70C. Basically you tell it what temperature you want on the outlet and it works as a ‘top-up’ heater to the extent required to deliver that. It will restrict the flow if 8.8kW isn’t enough power to achieve the target temperature at full flow.
So such devices are available - and there are even more powerful models in the Zip InLine range (but those need 3-Phase electrical connections). I suppose if a household regularly runs out of hot water and it’s not practical to install a larger cylinder one of these heaters could protect against the cold shower scenario but a heatpump would surely always win from a running-cost standpoint.