Chewy, they might tinker with larger rules to encourage a healthy league (e.g., NBL not requiring guarantees to keep some teams in the league), but as I said, specific instructions to one ref would stand out (e.g., Donaghy) and to multiple refs would be a risk of a serious leak that would potentially derail a league and everything that goes with it.
If teams make adjustments to the flow of the series it's because they're studying strategy and game tape, tweaking their game plan, rallying when threatened or feeling confident, etc. If there are consistent patterns, it's more likely because the home-away format is often also consistent and players are human in that they react to these things in a consistent manner.
A team is coasting with an easy lead you say, and the other team rallies, more energy, more contact, more calls from the refs needing to be made. That's sport! This ain't Computer Assistance in NBA Jam!
The baseball and basketball teams you described are seriously iconic and powerful brands. There would be more interests working towards higher spending than not - the player associations for one. The NBA tried to ditch the soft cap just recently and we had a lockout because the NBPA denied that! You cannot put that on the NBA!
You also can't use the Lakers and Celtics to argue for 50-50 calls favouring little Oklahoma City, right? The NBA would've found a way to get the Knicks there if it were so trivial.
The league would be hopeful of a longer series, definitely. But I don't think they'd interfere with something like refereeing as you described to achieve that.