Given that we already do it for the playoffs the logistics wouldn't be completely impossible. It would be a headache to coordinate but having a large number of teams involved gives you a decent margin of error. If 20 is too much, the # of post-split games could also be shrunk down to a point where it's easier to arrange.
We don't actually do it for the playoffs. The playoff schedule is worked out at the time of the regular season schedule and teams consult with their arena the possibility of dates and times they may need the arena if they make the playoffs. Arenas make huge money during playoff games and so accommodate by being flexible. Being that flexible for a portion of the regular season and the playoffs would be bad business and a logistics nightmare. Not to mention most arenas, especially for regular season games of bad teams versus bad teams won't make nearly the money they would for playoff basketball so there is no incentive for them to do it.
And as I have mentioned, the NBAPA would NEVER allow this to happen. NEVER. It could hurt the brand name of players that market themselves in other endeavors. Sooner or later the owners, who would also NEVER allow this to happen, would want to pay this players less when in the second division. The NBAPA would know this and strike the minute this became what the NBA was all about.
People need to realize that the professional sports model in America is different and has had no problem making gobs of money in a much more intensive and competitive market for sports dollars than European soccer. The anti-tanking agenda the league MIGHT someday have, because they really don't right now nor do they care to fix it, will be something that keeps their business model intact instead of completely ripping it apart and starting all over again. You rip up your business model and start all over again when the business model doesn't work. Everyone in the NBA is making huge cash. The business model is working fine and needs a tweak here or there, not a complete overhaul.