This has been something that has been bugging me for quite some time, as if you look at the role Avery has MarShon Brooks playing and you then look at the role Avery has Anthony Morrow playing it appears that their roles are reversed

MarShon had success early in the season because injuries allowed him to go through stretches where he could dominate the ball. The book on Morrow has remained largely unchanged since years past, give him a sliver of space and he can knock down a three with the best of them, but ask him to put the ball on the floor and you're going to be in trouble.
Right now as a member of the starting lineup MarShon is being asked to cut back on his isolations and act as more of a spot-up shooter - something he's not very good at right now - while off the bench Morrow is essentially being asked to carry / create for the second unit despite the fact that he struggles to create his own shot...
It just makes more sense to me to have Morrow starting so he can take advantage of Deron + Wallace's penetration skills and to let MarShon come off the bench and be the go-to scorer for the second unit...
:-/
(The only positive I can say about Avery's stupidity on this matter is that Morrow has developed a surprisingly effective game in the post. He only has 1 or 2 moves down there but he typically generates good looks from them, especially against smaller defenders.)