I enjoy your posts and respect what you have to say, but I think that you have the right conclusion for exactly the wrong reason.
It was never going to be about heart. This team was built on three hall of famers who all had the tenacity to build their games into something way beyond their talent and physical abilities alone. Then they had the tenacity to reinvent themselves for the sake of playing better together. They joined a point guard who folks said couldn't make it in the NBA because he couldn't shoot and didn't have the pedigree to run a championship caliber offense, who has now reinvented himself as the best passer in basketball and an above average midrange shooter.
The simple facts are that Allen is gone, and Garnett and Pierce are past their primes to the point where not only are their abilities fading, but the fade itself is accelerating. Pierce isn't taking bad shots because he doesn't care- he's taking bad shots because they used to go in. Garnett isn't getting beat because he isn't focussed, he's getting beat because he can no longer jump high enough quick enough to steal a lob away from Andre Drummond even when he is in a perfect position to do so.
Is heart the reason why Jeff Green isn't a better basketball player, despite his tools? Maybe you could sell me on that, but he still has never been a particularly good player. I guess if he had more heart he would work harder, focus harder, and make himself into one. In that sense, the problem isn't his heart now. The problem is that he hasn't had heart for his whole career.
Is heart the problem with Brandon Bass? Again, has Brandon Bass ever been a plus player? Over his career, he rates as an average player at best, and he was 1.5 points per 48 minutes worse than average last year, when by all accounts we were positively lousy with heart. He's a solid backup player... who ever thought he was going to be an impact starter?
Is heart the problem with Rajon Rondo? Let's remember how much Rajon Rondo is being paid before we go too far with that. Rondo is not a max player, though we continue to have those kind of hopes for him. He is a facilitator to the bone, and he has one of the most team friendly contracts in the league. Perhaps he isn't the leader or the alpha that the team needs, but he's our most productive player and he's an undeniable bargain.
Is heart the problem with the suddenly barely-average Jason Terry? Terry is the worst kind of aging vet- a small one. Size is the only thing father time doesn't take away from you. Undersized shooting guards are the least likely of all types of players to have long careers.
Heart makes for a good narrative, because none of us like talking about aging. This was always going to end, though, guys, and it was always going to be ugly precisely because they have so much heart. Heart made Kareem stick around until he could barely move. Heart made Larry play in a giant flak jacket. Heart made Brett Favre come back three times until he finally turned his narrative from "greatest qb ever" to embarrassment.
Pierce and Garnett will both look bad before they fade back into complimentary roles like most men their age, and it won't be because of their heart. This team is built to compliment KG, Pierce, and Rondo. It was never going to keep dominating when those guys were no longer capable of dominating.
So with all of that said, I do agree with your conclusion. This team will only improve going forward if Sullinger and Green can take the mantle. I don't think that is going to happen, particularly in Green's case. Blowing it up will be the right choice, probably, some day. Maybe today. I think that what is happening here, though, is a lot more dignified than what you are making it into.