I think there's one absolutely major factor that you're completely ignoring... one of the reasons the bench had to play so many minutes for the 2008 Celtics was because their three major stars were all over 30 (edit: looking at the number again the difference isn't quite as stark...they did play quite a bit of time). I don't think if Pierce, KG and Allen were in their mid 20s that the bench would have played nearly as much.
The current Celtics team has two players over 30... 2008 had 7. The stars of the celtics are in their primes more or less.. Holiday is a bit older. The bench is pretty much the same or younger. Cassell played a lot of minutes when he came over.. but 2023 has Holiday already. PP is basically House. Al is essentially Posey. The obvious main difference is that Tatum and Brown have to score.. Tatum especially. KP's numbers are similar to KG. DW is a similar to Rondo. Hauser, as others have said, plays more minutes and scores similar to Posey.. he's also on pace to play a lot more games in the regular season.
I think the other idea is that of experience... I haven't looked into the numbers, but I'd imagine the top six players have quite a bit of experience in the playoffs.. and I'd bet a lot more experience than the 2008 team at similar ages, but I'd have to look.
Minutes/Points/Games
Pierce (30) 35.9/19.6/80 - Tatum (25) 37/27.7/18 (extrapolates to 82 games) - Pierce played 39.2 mpg at 25
Garnett (31) 32.8/18.8/71 - JB (27) 34.5/21.9/17 (77 games) - KG played 39.4 at 27
Allen (32) 35.9/17.4/73 - KP (28) 30.3/18.9/15 (68 games) - Allen played 38.4 at 28
Rondo (21) 29.9/10.6/77 - DW (29) 32.2/13.9/15 (68 games)
Powe (24) 14.4/7.9/56 - JH (33) 34.5/12.4/16 (73 games)
Cassell (38) 17.6/7.6/17 - Hauser (26) 22.8/9.7/18 (82 games)
House (29) 19.0/7.5/78 - Horford (37) 25.8/6.9/16 (73 games)
Posey (31) 24.6/7.4/74 - Pritchard (26) 20.6/6.3/18 (82 games)
Perkins (23) 24.5/6.9/78 - Kornet (28) 13.5/4.6/13 (59 games)
Allen (26) 18.3/6.6/75 - Queta (24) 10/3.5/2 (9 games)
Big Baby (22) 13.6/4.5/69 - Banton (24) 8.8/3.5/8 (36 games)
P.J. Brown (38) 11.6/2.2/18 - Svi (26) 7.4/2.0/8 (36 games)
Pruitt (21) 6.3/2.1/15 - Brissett (25) 11.3/1.8/8 (36 games)
Scal (29) 10.7/1.8/48 - Stevens (26) 3.3/1.5/6 (27 games)
Pollard (32) 7.9/1.8/22
Edit 2: (it's sort of shocking that KG led all scorers at 20.4/game, Pierce 19.7, Allen 15.6, Rondo 10.2.. then a bunch of players in and around 5-6)
2008 in the playoffs:
Pierce 38.1
Allen 38.0
Garnett 38.0
Rondo 32.0
Perk 25.2
Posey 22.0
P.J 13.6
Cassell 12.6
Powe 11.7
Davis 8.1
House 7.9
Allen 4.3
In last years playoffs
Tatum was at 27.2 on 40 mpg
Brown 22.7 on 37.6
Smart 14.9 on 34
DW 13.4 on 29.7
Brogdon 11.9 on 24.9
RW 7.7 on 20.9
Horford 6.7 on 30.9
I think adding KP to replace Smart and Holiday to replace Brogdon should be adds...plus more minutes for White. As others have said.. having essentially 6 starters and Al before getting to Hauser and PP is a pretty big difference. Hauser should see a big boost in minutes from last year.
PP is a question.. but I think/hope that Joe and his assistants are mapping out how to use him in the playoffs...as well as other bench players as they see various matchups.
The main factor is that the top 6 have to be healthy and Tatum has to be playoff Tatum.
The main reason for the minutes distribution in 2008 was blowouts and Doc switching up bench minutes. It's really pretty simple actually. Outside of blowouts, the C's were playing a 7-8 man rotation.
Hawks series:
Game 1, win by 23: Cassell was the 8th guy at 16 minutes. Allen played 9 minutes (nobody else was above 4)
Game 2, win by 19: Glen Davis was the 7th man at 14 minutes, but you also had Powe at 13, Cassell at 11 and Brown at 9.
Game 3, loss by 9: Big Baby was 7th man at 16 minutes, Cassel was 8th at 15, Brown and Powe played 6 minutes each
Game 4, loss by 5: Posey was the 7th guy at 18 minutes, Cassell and House were #8 and #9 and they both played 6 minutes. Big Baby played 5 minutes, Allen and Brown didn't play at all.
Game 5, win by 25: Posey played 20 minutes as #7, Cassell got 15 minutes, Brown played 7 minutes, and Baby/Allen both played 5 minutes
Game 6, loss by 3: Cassell played 20 minutes as #7, Powe played 15 minutes. Brown played 4 minutes, the other 3 guys (Baby/Allen/House) played a total of 2 minutes combined.
Game 7, Win by 34: Powe played 22 minutes as #7, Brown played 13, Allen played 11, House played 10, Baby played 9...
Cavs Series:
Game 1, win by 4: Cassell played 18 as the #7, Powe played 13 minutes, nobody else played more than 4 minutes.
Game 2, win by 16: Cassell as the #7 played 25 minutes, Posey as the #8 played 21 minutes, Brown played 5:47
Game 3, lose by 24: Cassell played 18 minutes as the #7, Powe played 15 as the #8, Brown played 10, House played 6
Game 4, lose by 11, PJ Brown played as the 6th man in this one, and played almost 23 minutes, Posey played 19, Cassell played 14 minutes
Game 5, win by 7: Posey played 17 as the 6th man, Baby played 11 minutes, Brown played 7 minutes. Nobody else played more than 5:29
Game 6, lose by 5: House played 18 minutes as the 6th, Baby played 17, Posey played 14 and Brown played 8. Nobody else played, including Cassell, Allen and Powe.
Game 7, win by 5: Posey played 26, Brown played 18, House played 15, Powe played 6:37. Nobody else played, Cassell, Allen, Baby
I dont have time to do the other series right now, but eyeballing it, it's more of the same. Doc was constantly tinkering throughout the playoffs on who would play minutes coming off the bench on a given night, resulting in a bunch of guys with minutes, but the reality is every close game was a pretty tight 7-8 man rotation.