Could this be a combined Tatum-and-Brown-alpha-problem?
Remember the aftermath of the 2018 Playoff run? The next summer Irving and Hayward returned from injuries, but huge chemistry problems arose. The young guys (Rozier, Brown and Tatum) didn't want to go back to their previous status. Although it must be said Brown dealt really professional with his bench role.
In crunch time they didn't necessarily seek Irving for the final shot. We all know how badly Irving reacted to these changes, but he had a valid point that he should still be the number one option to create a shot. Even LeBron deferred to Irving in Cleveland.
Now we have a situation where Tatum and Brown have come of their best scoring seasons. The Celtics add Porzingis and Holiday, while White showed he could muster a bigger production. Instead of thinking how much easier these additions would make it for Tatum and Brown to have a good offense they may think it as a challenge how to push the new guys in roles that don't interfere too much on how they're leading the team as superstar scorers.
With a more passing orientated style it's a risk that capable guys (basically every possible starter) will find reasonable opportunities to take more shots which would naturally go at the cost of the very high volume guys. In the most extreme case like the San Antonio Spurs you'd have the team as winners first, while their stars (Duncan later on, Ginobili, Parker, Leonard) were almost an afterthought.
That may be an idea too tough to swallow for both Tatum and Brown, as they idolized Kobe Bryant. They want to be known in the headlines as "Tatum with Brown as co-star lead the Celtics to a Championship". NOT: "The Celtics win the Championship with Tatum, Brown and Porzingis, White, Holiday".