just competes against the regular playoffs. With 7 game series each round, there are already like a gazillion games on. So these draft tournament games would just be either getting minimal attention or drawing attention from other NBA games.

If you wait until the summer, then you are interfering with the player's offseason.

Even if timing were not an issue, I think it would be at best mildly entertaining. I don't think players themselves care that much what number of draft pick their team will get the next season.

Now maybe have the execs play a basketball tournament for the #1 seed in the draft. That could be interesting.