I like how the OP keeps ignoring the team dynamic this year is different than any year since Exum has been on the Jazz. No Hayward, no Hill taking the majority of the shots and Johnson and Gobert hurt adds to even more available shot attempts. Favors has been inconsistent, or disinterested in taking some of those now available extra shot attempts so that would've left Exum to see if he would be willing to take some of those attempts.
I think it really sucks that Exum is hurt this year, this would've or could've been the year for him to prove himself, I still have faith in him to turn out at the very least as a Shaun Livingston type of player (injured and almost forgotten but ends up proving to still be a good player with a long career). If he was healthy I would love to see what the DMX back court could've accomplished, Exum is much more of a willing passer (too willing at times) but that could be what would've helped that dynamic grow.
Lastly Donovan wasn't given permission by Snyder to take those shots, Donovan just took them cause he believed in himself (some times too much) and didn't worry if it was okay if he did. Yes he's (so far) been inconsistent and a lot of games not efficient in his scoring but such is the life of almost every rookie in the NBA when they are seemingly a teams top 1 or 2 scoring threats on most nights. Again that feeds into what I first said Exum never had this opportunity because of the team dynamic that Donovan has. Although to be fair to Donovan he still would've never asked for it he would take it either way until the coach sits him (which is what would've happened if Hayward was still here) because he just has that killer instinct in him and its seemingly the only way he knows how to play.