Um, the Cavs only played 8 players in game 7. Smith played 42:26, Hill played 38:02, and Clarkson played 9:20. Korver played 17:36, but most of those were at the 3/4. The other bench player was Nance who played 7:51. Lebron played the entire game. Jeff Green played 41:54. The other Cav, Thompson played 34:51.
Now sure, Boston played just 7, Tatum led the team with 42:09 (so less than James and Smith and barely more than Green). Horford was next at 40:11 followed by Brown at 38:56, Rozier at 36:16, Morris at 32:50, Smart at 30:50, and Baynes at 18:48. Baynes obviously didn't play very much, but combined played more minutes than Clarkson and Nance.
The reality is the Cavs played more minutes from their starters than Boston did (even counting Morris instead of Baynes that is still true), and while Cleveland played the extra man, the Cavs bench players collectively just didn't play all that much, which strained their starters even more.
It is nice to think that Jabari Bird would have made a difference, but at the end of the day, Boston lost because Lebron James was on the other team and Boston just couldn't stop him from scoring 35 points (on 50% shooting), grabbing 15 rebounds, and dishing out 9 assists. Jabari Bird wouldn't have made a difference against Lebron James, so he wouldn't have made a difference in that game.