Murray got the ball plenty when Brees was out. Think he had three 100 yard rushing games or so during that 5 game stretch Bridgewater started.
This goes back to "Was Brees switching out of the run" audible when he came back. Not a coincidence that Murray ran less when Brees came back. Bridgewater wasn't changing plays.
Having Murray run more wouldn't helped Kamara who obviously was hurting.