If you want the shower to save your temperature preferences and start automatically, there’s no reason to build in a computer capable of running an AI.
But in reality you almost certainly don’t want a system like this because you don’t want an AI accidentally turning on your shower when you’re not home, when you do ok to clean it, or grab a razor, or when your toddler wanders in.
Granted an AI could try to determine intent, but it’s never going to get it 100% right. Which is why for physical systems like this you almost always want a physical button to signal intent.
Also that sounds like an awful lot of computing power for everyday UIs. It also doesn’t solve the non determinism problem.
There’s no way to use fewer actuators, and the control system is already dead simple, and uses one temperature sensor per outlet.
Who knows, AI can come up with simpler or cheaper solutions that did not cross our mind. I would say, time will tell.
The lack of AI isn’t what’s holding back your dream of a temperature controlled shower in every house.
That exists, but it’s expensive because of the electronics and mechanics involved. There are so many interfaces with this exact problem.
You also almost certainly don’t want non-deterministic hallucination prone AI controlling physical systems.