After a full season sample, it's obvious that the pieces just don't fit together from a basketball standpoint. The drama of the regular season and pressure of expectations only made things worse.
I'm mainly referring to the dynamic between Kyrie, Brown, Tatum, and Hayward. Each of these players is at a different stage of their careers, and none of the final three were in a position to elevate their games to an All-Star level. As others have mentioned, there was no hierarchy of roles. Hayward couldn't find a consistent middle ground between aggression and passiveness, and Tatum clearly suffered from overconfidence after the playoff run from last season. I'm not so sure this group would have made it work even if the roles were clearly defined.
Jaylen Brown deserves the most credit for finding a niche with this team, especially given the uncertainty surrounding the group. He was able to provide a positive impact regardless of usage.