The "Spurs model" is dependent on the key player maintaining a high level of play.
Tim Duncan is still a 20-10 player at the age of 35. Even so, the Spurs aren't really contending at the moment. They won a few times in the last decade when their players were younger than the Celtics players are now.
KG is obviously not still playing at a high enough level. Pierce has lost his speed and athleticism, and even Ray is having trouble staying consistent from outside.
The Spurs have also benefited from very good drafting and free agent signings. They've been able to find role players that fill well in their system to complement their core. The same can't really be said of the Celtics in the last couple of seasons
A rebuilding process will certainly take a long time, but the only alternative is staying mediocre (~40ish wins) for the next ten years by trying to build around Rondo, Perk, free agents willing to come to Boston, and middling draft picks.
Though it will put us through some tough years, in the NBA the only way to really rebuild is to give away all but the most vital assets and tank for high draft picks, unless you're lucky enough to be in a city where big name FA might actually want to go.
All of the current "elite" teams (Cleveland, Orlando, LA, Denver, Dallas etc) all had to endure periods of dire mediocrity and then get lucky enough to pick a superstar around which to construct a team - well, except for the Lakers. LA has the luxury of being a super rich team with the ability to lure FA and swing lopsided trades. The Celtics have no such luxury.