AndThe league could institute their own "National Match," where teams and players were wed based on mutual interest. The NBA could have teams bid on draft slots. Some have proposed an auction system used by many fantasy sports leagues, in which a prospect is assigned to the highest bidder.
Novelty has its appeal, but addressing the inherent inequities of the draft might be best addressed by Occam's Razor -- simply declare all eligible incoming rookies free agents.
We have no idea where Davis would like to work if given a voice in the matter. Is the Chicago kid someone who wants to stay close to family, even if it means taking less money or playing in a small market like Milwaukee? Would he and his representatives approach the Heat, the big dogs in the East who could use a center, even though Miami couldn't offer the money or touches Houston could? Maybe there's an NBA coach who dazzles him with the power of persuasion, or a team that could pair him with a dynamic point guard, like Cleveland. Then again, maybe Davis just wants to go where he can make the most money -- playing time, viability, co-workers and geography be damned.