You bring up a good point. The Big Three indeed could be good for quite some more time. However, pulling out names like Jordan and Malone really represent ideal scenarios. It could happen, but is not incredibly likely. And while some have tossed Bird's name around, the fact of the matter is that the wear and tear on Bird ultimately lead to a debilitating injury to him in his early thirties, and that could certainly happen to any of the Big Three at any time.
And therein also lies the problem. They are "The Big Three" to an even more literal sense than the original one. Whereas if you looked at Bird, McHale, and Parish, Bird was clearly the dominant, "player for the ages" amongst them. With the current Big Three, none of them are as good as Bird, and while Garnett would be the likely pick for the best of the three, it's not nearly as clear cut. Simply put, if one goes down with a long term (or worse, career ending) injury, that could be the end of championship hopes. You could argue that if Parish went down, and Bird and McHale were healthy, they'd still be contending.
Also, I think Nick overexaggerates some of the players' accomplishments:
Shaq was a shadow of his former self in his championship in Miami, as he was arguably the third most valuable player in the Finals after Dwayne Wade and Antoine Walker of all people.
Hakeem did win his titles around the time the Big Three did, but he was in decline by 34 and a shadow of himself by 35. More importantly, he never saw the Finals again after 32.
The Admiral wasn't even the same player in 98-99 with his first title at 33 as he was just a few years earlier. More importantly, by his second title 4 years later, he had declined to the point of being little more use than your average NBA center.
So while I grant you that it's certainly possible that the Big Three could be still could for quite a few more years, I would also saying that using Jordan and Malone as examples of why it could happen is about as good of a reason as saying that the #3 pick in the draft will also be as good as Michal Jordan simply because they are both #3 picks. Jordan and Malone were freak picks at their give positions, just as Jordan and Malone were athletic freaks for staying in shape so well over their careers. It could happen for our guys, but I wouldn't bet the house on it.
What does that mean? Not too much. The only thing I'd take from that is simply that Ainge should be doing everything in his power to win now. Developing the youth should only be done if Ainge seriously thinks they can help this year or next. If he thinks a player can't help for 3 or 4 more years, he should be stashed on the end of the bench, IR, or cut.