I am putting in a backsplash in my (rather old) kitchen with white subway tile. My dilemma is around the stove, which is in the right corner next to a cabinet wall. What I've seen and read suggests that it looks better not to put backsplash on a side wall.

However, the cabinet wall is right beside the stove and the wall is quite beat up. The side wall is not in view when you enter the room, primarily when you are standing at the stove.

In this situation would it be worth it to wrap the backsplash around the corner and onto the cabinet side wall?

This is the damage on the side wall.

Thanks for your advice!