This is also the case for electric showers though, where the shower itself contains the heating element and heats its own water, rather than taking arbitrary feeds of hot and cold water.
The shower doesn't need an internal heating element. All you need is an electric control system, which dynamically monitors the temperature coming out of the shower head and constantly adjusts the mix toward a set temperature.
I have a feeling these have existed for a long time in Japan.
You don't even need an electronic thermostat. You have manual thermostatic valves that do the same thing. I believe it has to do with the thermal properties and mechanical interface of a couple pieces of metal. As they expand or contract, it adjusts the mix to maintain the temperature set by the position of the handle.
