So, you penalize Utah for 20+ years of success and reward Orlando, Charlotte, and Cleveland for sucking? That's not fair.
The really lousy teams would still get the best shot at the top picks. But they would have no incentive to out-stink each other. That would mean that, when general managers constructed their teams over the summer, they would be more likely to add a player or two that would improve their team, because the downside risk (losing ping-pong balls for the lottery) would not be there.
This would also help take care of the perception problem. Once the season was underway, there would be no question: The players on the court would try to win. So would the coaches. This would make the worst teams more watchable, which would be good for fans, and good for the credibility of the league. There would still be bad teams, but that's true in every league. You just don't want anybody thinking it is good to be the worst.
The teams in the upper tier of the lottery would also be unlikely to tank. They would have too much to gain by making the playoffs, even as a No. 8 seed: at least two home games' worth of revenue, positive publicity with the fan base, playoff experience for younger players, and the once-a-decade chance of pulling an upset. That's not worth giving up for a two-percent chance at the No. 1 pick. That's why the bottom half of the lottery would be weighted -- you can't have teams bailing on a playoff race.
Oh, I suppose that in the final week or two of the season, teams that have been eliminated from the playoff hunt might tank, to slightly increase their lottery odds. But they would be tanking a game or two. They wouldn't be tanking the whole season.
Some general managers would still decide to rebuild by trading their best players for draft choices and young talent, and to free up salary-cap space. But that falls under patience, not tanking. You see similar moves in other sports.
Teams are like people; for the most part, they act out of self-interest. The NBA just has to make sure it is not in team's best interests to tank. A simple tweak of the lottery would help.