My thinking is that copper could look distinctive and unusual. I know that copper has been used to make bathtubs in the past.
I believe it has the potential to be waterproofed if the corners of the sheets of copper are welded together. But beyond that I have no idea if it can be waterproofed if the metal has to get bolted into the wall.
I think copper could be cheaper to use than granite or some other stones.
Finally, I am trying to think outside the box, no pun intended.