I think every time Patty has been left on the bench during a Parker injury, there's been a good reason. Earlier in his career, it was that he wasn't much of a playmaker and without Kawhi having developed that side of his game, the starters needed someone who could create more than Patty. He benefited from playing next to Manu in Spurs bench lineups.
Now he has improved, the Spurs have less point guard depth, Kawhi is a capable playmaker in the starting unit, and Manu is, well, old. So the starters can carry Murray, whereas the bench could not.
I actually think Patty has filled either the role that suits him best or that the team most needs, in both situations.