I'd much rather have Bynum than Lopez, Humphries, Brooks, and two #1's. The second best center in basketball, or 5 players who are likely to combine for 0 all-star appearances for their career? I'll take the second best center.
You are overrating the importance of depth and a bench in the playoffs. Know how many players scored for the Celtics in Game 7? Six players. Know how many players scored for the HEAT in Game 7? Six players.
No one is saying Nash is going to play more minutes than Rondo. That is absurd. There is a big difference between barely playing half the game and playing more than Rondo. By your standards, KG and Pierce barely play half the game.
Once again, all of your points are a severe stretch.
You'd rather have a known headcase and historical injury risk than 3 guys who combined to average 55.6 pts and 18.2 rebounds last season, in addition to two first round picks? I'm sure a lot of GMs think like you and that's the reason so many teams NEVER win championships.
And on the subject of draft picks, LA traded their first rounder this year for Ramon Sessions. Since he's almost certainly not back next season, that means they traded it for nothing since they could have lost in the playoffs just as easily with DFish.
Who did Cleveland get with LA's draft pick? Jared Cunningham. Who were some of the players selected after that pick? Tony Wroten, Perry Jones and Marquis Teague. Some people wanted Ainge to take Jones instead of Sullinger or Melo. The Lakers gave away the chance to get Jones or Sullinger or Melo in exchange for a total of 35 games of Ramon Sessions.
As for minutes, KG averaged 36.9 minutes in the playoffs and PP averaged 38.9. Again using the Rondo regular season comparison, how many times did Pierce play more than 36.9 minutes in a game? 19. KG did in 8 times. Nash? 4 times. Again, how many minutes is Nash going to play in the playoffs next year for LA and how many minutes will they have to go with Steve Blake?
Mike
Yup, clogging your cap space with a player like Brook Lopez, who averaged under 4 rebounds last year is a great way to win a championship! And two late first round picks! And Marshon Brooks, a gunner who shoots around 40%. To use your exact quote, I'm sure a lot of GMs think like you and that's the reason so many teams NEVER win championships.
You do realize that if they acquire Lopez and Humphries they have to overpay both of them, right? After all, Lopez and Humphries have to agree to go there in a sign and trade, so they have to be the highest bidder. Otherwise, Lopez and Humphries will sign elsewhere. If overpaying role players is your championship formula, you need to rethink it. Teams that overpay role players definitely win more championships than teams that have elite big men. 
Nash's most recent playoff saw him play 37 minutes. He played 32 last year in the regular season. There is no reason to believe he can't play in the 35 minute range, which is more than half of the game, by the way. Half of the game is 24 minutes.
Brook Lopez' career averages are 17.4 pts and 7.5 rebs. Bynum averaged 18.7 pts and 11.8 rebs last season. Kris Humphries averaged 13.8 pts and 11 rebs this past season, 10 pts and 10.4 rebs the season before that. Yes, Bynum is the best individual player but you can already argue that Lopez and Humphries combined are better than he is alone. Throw in Brooks, who more than a few on this board were upset that Ainge didn't take in the draft, and two future picks and the Nets package only gets stronger. And that's without factoring in Bynum being a headcase with a history of injury problems.
And Nash's last playoff run was two years ago. He averaged 33.7 minutes. Do you think he can play even that much three years later?
Mike
You are ignoring the fact many things in that post.
You are ignoring that Lopez and Humphries are both free agents. In other words, you will have to be the highest bidder (overpay them). Otherwise they will sign with other teams as a free agent.
You are ignoring that they will take up 2 spots in a starting lineup. The Magic can put another player in at PF, so totaling production doesn't make sense.
You are ignoring that these guys put up big numbers on a bad team. Lopez, Humphries, and Brooks put you so close to a championship, that adding them to Deron Williams (one of the best PGs in the league) wins you about 20 games. Why is this? Will the Magic have a better PG than Deron Williams?
Isn't acquiring the core of a 20 win team without its best player a recipe for 20 wins?
Why not trade for Bynum and sign players equal to Humphries, Brooks, and the two #1s in free agency? Which should be very easy to do. You can cherry pick good 1st Round picks all you want (or guys that you think are good 1st round picks) but there are bad ones too.
Believe it or not, some of those guys you named will end up being unproductive. It happens every year at the bottom of the 1st Round.