I read this theory all of the time. The Bulls should throw in the towel on this season and rebuild around Rose. There are several problems with this theory, but the biggest problem is that they already missed their window of opportunity to do it. Attempting it now would provide a half-assed attempt that would not facilitate rebuilding but only weaken the team.
The case for tanking
There was a case to be made for tanking. The time to make that case was in the summer. If Chicago looked at the NBA landscape and said, "We're not reasonably going to compete with the Heat for at least two years, let's aim to rebuild in the third year and do it right now." then they could have made an attempt to rebuild from scratch.
Trade Luol Deng for Harrison Barnes and Richard Jefferson? Done.
Move Taj Gibson for a draft pick? Done.
Swap C.J. Watson for a pick and contract (done, and they had this option for awhile, but it expired after Jarrett Jack fell into Golden State's lap).
Trade Korver/Brewer to Detroit for Ben Gordon and a draft pick, done.
Force Derrick Rose to sit out as absolutely long as possible [still likely couldn't sit him all season] done.
What would the result of this team be? A crapload of young players, future picks, and only Joakim Noah and Derrick Rose on the books in three years (Boozer would likely be amnestied in the final year of his deal to be off the books that year). Chicago would then have oodles of cap space, and lots of bullets in the next few drafts [though they'd be shooting bullets out of a pistol aiming for targets at rifle range].
They'd also be bad enough to likely pick in the top 5-6 this season.
You do all that and hope that you luck into some good players late in the draft simply due to the number of opportunities you have. I don't think it would be likely to work, but it was a somewhat viable plan that could at least be argued for. You'd grab a ton of draft choices to go with a team that would have the cap room to absorb contracts or sign free agents in a couple of seasons.
You'd also probably lose a tons of money over the next two years (that's a Jerry Reinsdorf no-no), enrage the many fans who actually want to see the Bulls win, and alienate veteran players who wouldn't understand why you blew up the team. However, in the long run, the plan would have some chance of success as long as you hit big on your early pick and drafted good players with your mid to late 1sts and 2nds.
The case for not tanking this summer
Even if you do all of the above, you're not likely to get the difference making lottery picks that land you a superstar. Once Rose is back tanking will be out of the question as he'll single handedly get the Bulls too many wins to finish in the bottom five.
All of the picks you get via trade outside of Harrison Barnes (or whomever you'd have taken with the GS pick) are likely mid to late 1st rounders and unlikely to yield anything better than role players. The Bulls would count themselves lucky to simply get players as good as Taj Gibson and Luol Deng back with these picks.
In the end, getting a second superstar wouldn't be likely, and they'd look like a farce to players around the league further hurting their ability to recruit players to come play here. It'd effectively be a hail mary that would only work out if they were able to delay Rose's return long enough [don't underestimate how hard Rose will fight you on this and the PR battle you'd lose if you tried to stop him] to ensure a top pick next year and then got your star.
Those are long odds, since Rose will probably be back for half the season, next year's class isn't loaded with stars, and the Bulls would probably pick outside the top six slots.
For making this hail mary, you'd alienate your fan base, alienate yourself from veteran players, and lose a ton of money.
I'm not surprised (or upset) that the Bulls didn't make that attempt.
That was then, this is now
The case for tanking back then was somewhat flimsy. The case for tanking now is eye-poppingly bad. I've heard people say things like "tell Deng he has to get the surgery and fake an injury with Joakim Noah". Really? REALLY?
You're going to go to a player and force him to get surgery? You're going to tell Joakim Noah that he can't play? You do realize that these players believe they can win right now right? You do realize they have pride and want to win right now right?
No one will go along with this plan. It will (obviously) leak out what's going on as the players will go right to the press and bitch out loud about how the Bulls don't care about winning and want to throw the season. There's a good chance the NBA straight up sanctions them for even attempting it in such an obvious way.
Why don't we go ask Derrick Rose and Tom Thibodeau what they think of the "tanking" plan and see how it works out for the coach and franchise player. I'm guessing that it won't be viewed too favorably, but that's just me.
However, let's move beyond the fact that there's no reasonable or rational way to pull of this plan at this point anyway and assume against all evidence that everyone on the team is willing to go along with it.
The Bulls already missed the window.
If you wanted to reposition the team to rebuild then you don't sign Taj Gibson to a four year deal for over eight million per year. You're not getting a 1st rounder back for Taj anymore now that he's at the high end of his market value for four seasons.
You're not likely getting a lotto pick for Luol Deng with only one season left on his contract from someone in the summer.
All the guys you could have traded away to bring back additional picks by taking on short term bad contracts are gone and can't be traded away.
If you attempt the tank plan now, you're going to do it without Detroit's pick for taking on Gordon, without the #8 pick in this year's class you could have had for Luol Deng, and without the mid to late 1st you would have had for Taj Gibson. You're going to do it without as much salary flexibility to make unbalanced trades, and in effect, you're going to be doing it completely half-assed.
The original plan likely wasn't going to yield a better team than what the Bulls have now. The completely half-assed version of the plan is assuredly not going to yield a better team than what the Bulls had now. Whatever window the Bulls had to attempt a successful complete rebuild and roster turnover is closed.
Chicago will need to look to trades, MLEs, and the future assets they have to improve the team incrementally from where it presently is. For better or worse the complete rebuild train left the station on draft day when the Bulls didn't make any moves.
Chicago's still positioned well if Rose makes a full recovery
The hardest thing to do in the NBA is get a superstar. If Rose recovers fully then the Bulls still have one which puts them in better position than 25 other teams in the NBA. Yes, it will be extraordinarily difficult to put together a team to compete for the championship, however, stop and think about how hard that is regardless.
Is there any reasonable way that a team can build to have more talent than the Miami Heat when they turn it on right now? The Lakers added Dwight Howard and Steve Nash to a core of Kobe Bryant and Pau Gasol, and I still think they're significant underdogs. The Bulls only play to get on the same level as the Heat was to get Dwight Howard themselves, and Dwight Howard made it clear he did not want to play here.
Once Howard passed, Chicago's best hope is to simply build as good a team as possible and get lucky. Sorry folks, if there was a reasonable plan that landed them a second and third star player to matching the Heat's talent level then I'm pretty sure the Bulls would already have taken it.
However, there's not. There's no reasonable "get two superstar" plan available. Only one in 5-6 teams has a single superstar, so to get two is a daunting task with no obvious path from here to there.
The Bulls have a very good team. They need to add talent to it to seriously compete for the title, but tearing it down is far more likely to waste two years and build up to something that's not as good as what they already have. I don't like their odds moving forward, but I like them more than pissing away two years on an attempted rebuild and hoping for the best. Especially since we'd be doing it with three or four less first rounders than if we attempted it five months ago.