I imagine that it would be difficult to keep properly clean. In the kitchen, the best way to keep stainless steel clean is with regular application of WD40 as a cleaner and a prevention agent.
Keeping stainless wall in a bathroom "touch-free" would be almost impossible, I also have no idea how much a large sheet of high-quality stainless steel would cost.
That said - there is another backsplash material that is perfect - glass. I am currently oscillating between a glass wall and a large-format tile (1200x1200) to avoid as much grout as possible
It would be interesting to spec. the cost of all three as an exercise - I've been unable thus far to get an estimate online without submitting an email address.
Regards
Tet