I actually like a slight modification of Simmons' proposal - top 7 make the playoffs, the other 8 in each conference play a single-elimination tournament for the 8 seed. Every team outside the top 7, including those 8 seeds, gets one ping-pong ball, but only the top 4 are drawn, and the other picks go in reverse order of record (worst teams pick higher).
Everyone outside of that top 7 has an equal chance at the top picks, but the really bad teams still are a bit closer to the top of the line. The only real perverse incentive there is that some mediocre teams might try to drop out of the top 7 in the regular season and bulldoze the tourney, but that's a tough bet to make.