If we're talking about this year's draft, I wouldn't expect that the league cares where Ace Bailey, VJ Edgecombe or Tre Johnson end up. If they care about where a player goes, it will be Cooper Flagg, and it will be either an effort to get him to a big TV market so they can feature him in national game broadcasts, or get him to a franchise where they are confident that he can be successful (or both).
I wouldn't underestimate how significant Flagg is for the league as a TV product. He's the clear-cut #1 prospect, and he's the first white American elite prospect in I don't know how long. If the league thinks he can become "must-watch TV" for the casual fan, I could see them being tempted to tamper with where he goes.
The other thing I'd predict the league would be concerned about is the Oklahoma City Thunder, who are positioned to dominate the Western Conference for the next several years. Does the league want the Thunder to get another lottery pick from Philadelphia to add to their arsenal, or will the league make sure that the Sixers, who just had a dreadful season, keep their pick one way or another?
Then I guess the last question would be whether the situation in Dallas is so bad that the league has to give them a top-4 pick to get their fans to rekindle some hope for the future. But I'd kind of doubt that.