Just my opinion, but I don’t think he needs to show he can be a better distributor to get drafted. The NBA is full of guys that have at least one elite skill... Carr’s most likely role in the NBA, based on his past play and the fact that he’s not yet drafted, would be a bucket getter off the bench. Which he is currently very good at in the college ranks.
My thought is he just needs to prove he’s not a complete liability on the other end of the court and can be a net positive. Not a great comparison of styles/skills, but I look at a guy like Brynn Forbes on the Bucks. One of the best percentage 3 pt shooters in the league and part of the Bucks typical rotation. The bucks found a way to hide his deficiencies most of the year, at least until playoffs hit and he was forced to switch on to Young, Irving, Harden, Booker, and Paul. As long as Carr’s flaws don’t blow up the defensive game plan, his scoring ability should be attractive. The league has several sixth men type guys that simply come in and put up shots for the second unit... that’s more of the role I would predict.
proacitve edit:
Also I realize that Chris Beard isn’t going to sacrifice wins so that Carr gets his route to the NBA. His role on Texas may require a more balanced offensive approach. Carr was more than willing to distribute to Oturu but less so to guys he didn’t think could make a play. I suspect he will more readily share to the rock at Texas.