Wasn't actively posting at this point so I'll admit I just brushed past it in catching up with the thread.
It does mostly achieve your stated objectives of keeping the average good pick going to the worst teams, but rewarding the best teams with the best chance at the top 5, which would incentivize mediocre teams still pushing hard to win, to a certain point.
I think it pushes the idea a little bit too hard. While its true that many of the best players were drafted outside the top 5, its also true that you are way way more likely to find a great player in the top 5 than at any other position. So I think it becomes really difficult for really bad teams to pull themselves out of that hole. The occasional win for teams near the top is going to push a championship favorite to an untouchable decade-long juggernaut at some point.
I have generally heard that home court advantage in the NBA playoffs has become less and less important, which is one of the things that has led to teams resting star players a lot. This gives a little more incentive for them to do that. Towards the ends of seasons we may see teams near the tops of the standings rest players a little more, since dropping from a 3 seed to a 4 seed isn't going to matter too much for the playoffs, but gives a decent boost to the lottery odds.
Making the middle the "best" place to be is kind of interesting. The way you would see team churn would probably involve the big markets mostly hanging out near the top and reloading via free agency, occasionally dipping into that middle tier when players retire, and then bouncing back up either through draft luck or free agency. You'd see a lot fewer teams completely gutting themselves when they lose their big guns. I think it would be even more devastating to smaller market teams when their big name players leave in free agency. There would still be a tier of teams without hope of getting into the sweet spots that would probably still field very uncompetitive teams and decide they are better off losing for that 6 spot than trying to claw their way up the charts.
There's probably some equation that balances the relative value of a #1 pick vs the value of lower picks. Though the details of that would probably vary between draft classes, someone is going to run that on this chart and find some "expected maximum value" slot and the dominant strategy is going to end up being trying to capture the 7 or 8 spot, which is going to end up with some weird situations where teams above that slot are tanking and teams below it are trying to win.
I dunno, its an interesting idea. I'm probably not seeing everything with it. But gut feel, its going to create a scenario where top tier playoff teams rest the superstars more frequently, and maybe even intentionally tank a bit towards the end of the season, and mediocre teams try a weird combination of tanking and competing to try to reach a specific number slot. And some lottery luck is going to end up creating a superteam, with the odds of that happening to someone probably favoring the bigger markets