My background is in embedded systems. There is absolutely no way that an AI could make a temperature controlled shower cheaper.

There’s no way to use fewer actuators, and the control system is already dead simple, and uses one temperature sensor per outlet.

Temperature can be measured in different ways. IR radiation and sound can be measured from a distance. The relationship between temperature at the source, of the water exiting the showerhead and time can be learned. Water can be heated in different ways. The valve could also be a pump. Our reaction to the temperature of the water can be sensed.

Who knows, AI can come up with simpler or cheaper solutions that did not cross our mind. I would say, time will tell.

AI might also invent sonic showers, or teleportation to beam the dirt away.

The lack of AI isn’t what’s holding back your dream of a temperature controlled shower in every house.