We have a very short quartz backsplash around the perimeter of the countertop in our vacation home. It extends up to the bottom of the vent hood behind the range. I believe that when the vent pulls air up from the stovetop, it also pulls up grease. Therefore, I think the backsplash should be higher than twelve inches if you have a range hood. I don't know about code for flammable surfaces behind a range, which may also be an issue.

BTW, your inspiration pic is lovely.

I think that's a great concept for the kitchen and other rooms too.