I trained as an industrial electrician when I was younger so I have some tangentially related experience (though a lot of my apprenticeship was done in a flour mill which is is a very hazardous environment (fuel/air explosions are no joke)).
The conclusion I came to is that while some of the stuff is fairly trivial (constant temperature control for example requires some finesse when you have variable water pressure/flow rates but is solvable) other stuff is actually quite difficult.
How do you handle control inputs?
While waterproof touch screens exist they are ferociously expensive and look more at home in abattoir than a typical shower. So the control would have to be either very simple or controllable from a phone which imposes it's own problems (you would have to run the program before getting in the shower unless you want to take a shower with your £500 iPhone).
In addition there are liabilities (if your software goes rogue and melts the skin of someone that is probably not a good thing).
Safety Standards for showers are rigorous.
Standard for showers are already pretty rigorous (unsurprisingly as they combine electricity in close proximity to water and just for fun throw in scald and slip hazards) so getting a device certified may be expensive.
Integration
The shower would have to be manufactured with the "nest" style controller in it already, modifying an existing shower isn't go to fly as internally there are few standards (except across manufacturers) and anything that impairs the seal is going to get you sued.
None of this stuff is unsolvable if there is a market demand for the product but to be honest I'm not convinced there actually is.