One "problem" there is it goes right back to the rigged lottery theory where Ewing went to NY that lead to the weighted lotto in the first place and created the mess. Especially when maybe there is an argument NOT to give top picks to teams that are going to ruin potential stars.
The rigged lottery theory is that the NBA *League Office* wanted Ewing in New York for ratings purposes. On the other hand, *Team Front Offices* in a team-by-team vote will probably be less likely to send top picks to NYC/LA/Miami, etc. even when those teams are bad because the turnaround path for those teams can be so short. And of course, there's no reason why the vote couldn't be public.
I guess there's an argument for not wanting to send star players to the bad teams that could potentially ruin them, but if you set up a system that accomplishes that, then you're almost certain to create an underclass of say 5 teams that has very little chance of ever breaking out of the cellar. I don't think the NBA wants that from a competitive standpoint. If there were a plan for a B-League and metric-football-style relegation, then I think a proposal like that is more palatable.
I am a little more partial to some 3-5 year aggregate or consecutive missed playoffs if we want to just give it to the team in the most need.
I agree that this seems better than using a single-year record, but I think it would have to be combined with some sort of system that locked teams out of, say, the top four for a year or two after hitting the lottery, or you'd get situations where the Cavs land LeBron and then have top five picks for the next two or three years because their aggregate record remains poor. Unless that's the sort of thing you really want to see, but it would encourage 3-5 year tanks instead of just one-year tanks, and that could really get ugly.
Oh, and in case it wasn't clear, my suggestion is not that the front office vote sets the lottery, but that there is no lottery at all and the front office vote sets the pick directly. This sort of system would be able to immediately react to the results of the previous year's draft, so it wouldn't have the "lag" that a 3-5 year aggregate record would likely have.
Conversely, I'm also not entirely opposed to a tournament for the top pick. Instead of putting the top 3 guys with the worst team each season, why not put them with the team ready to take the next step? That might actually make the league more competitive as a whole. Especially if you seed the tournament for the top pick based on record and only award it to the top 2-3 (maybe 4) teams, and then give the rest of the picks in order of finish, there would be tons of incentive not to have the worst record but also plenty to have the best non-playoff record. Maybe?
I've never quite understood the proposals that suggest the tournament style you discuss here. The entire point of the lottery since it has been instituted has been to "reward" the worst teams because they need the most help, with a randomization component that was designed to discourage outright tanking (but which seems to not do a great job of that). Tournament suggestions (or others that reward the best pick to mediocre teams rather than the worst teams) seem to completely turn the rationale of the draft order as established over the past few decades on its head. I really thought most folks agreed at a basic level that the best picks should go to the worst teams, and the majority of discussion surrounding changing the draft order mechanism revolved around eliminating tanking. Then people start embracing tournament-style solutions that eliminate tanking, but do it at the expense of overturning the rationale of the draft and potentially creating a permanent underclass of teams. And I just don't know if people really want to do that, or if they just see a clever mechanism that discourages tanking and favor the bright shiny new idea without considering the other consequences of it.