I don't see how you can separate injuries and age.
The only reason we were able to acquire Allen and Garnett is because they were on the tail end of their careers, when injury risks are higher.
So, having gotten through fifteen player-years with the Big Three, and losing only three of those (two for KG, and one for Ray) to injury is about what you'd expect. Maybe even better.
And as far as other injuries (Bradley, Perk, Green, Wilcox) - I don't know that we've been more injury-prone than any other team. Look at LA with Bynum, or Chicago with Rose.
Where I think we went wrong, and I've said this before, is in signing bench/supporting players who were also old (JO, Shaq) or injury-prone (Daniels, Delonte). We needed guys who could play a lot, even if they were less talented.