Very little continuity which would affect teams and in turn the league/quality of play negatively, it would remove professional freedom from grown men, and for lack of a better phrase-it's just corny as hell.
If anything there should be more incentives for players to remain with their original team.
Some ideas I thought of very briefly before to help the competitive balance and just make the league more interesting:
They should put some kind of rating/tier system for players in place and each team should only be able to have so many tier 1 players, or even like a rating system 1-5 and each team can only use like 23 pts total. Say KD and Steph are both 5s Klay is a 4 and Draymond is a 3, Golden State would have used up 17 pts already on 4 players and then have 6 pts remaining for 8 players so they'd have all scrubs, maybe even like D league level players could be rated a 0 so they could use up 2 pts for a starting center (19 pts total) then have 4 pts left for 7 players and be forced to fill out the roster with a few scrubs and D league players. Obviously that's a very rough idea but I think something like that could work to make the league more competitive.
They could also make like half of each team's games at neutral sites so a teams location wouldn't doom them to mediocrity or worse. Imagine if the month of January the Western conference played in Europe and the East played in Asia or Africa, then they switched in March after a month back in the States in Feb. The game would be truly international, and everyone would be on a level playing field in terms of location. Again the logistics would obviously have to be extremely well thought out but I think something like that could be really helpful and exciting.
Last thing I'd suggest, and I posted this on here before, is a tournament style standing system. Say after 20 games the bottom 7 teams moved into the B division, then after another 20 games the next 7 teams moved down into the B division. Then there's essentially a 42 game tournament between 16 teams in the A division to see who gets to compete for the Chip. Every game matters in a system like that. And the B division keeps playing too and now you have 2 NBA Finals series. You could even rework the draft around this somehow. Make it like the B division is playing for the 1st pick, but the better the team is the less points they have to use up on their players (in the earlier proposed tier/1-5 rating system), so the worst teams would have an advantage at adding a superstar or two and some solid role players in the offseason, and there'd be less incentive to tank (some teams would probably tank to drop into the B division and play for the top pick)
So for example right now the Nuggets and Heat would be playing for the 1st pick, but the Nets, Lakers, 76ers, and Suns would have the most pts to use up in free agency, while also having a top 14 pick.