As much as I love Tim, I'm afraid he's the primary reason for Tiago's lack of playing time. I believe Tim (prideful, prima donna, whatever you want to call it) still wants to be THE GUY in the middle and doesn't want to share the stage with Tiago. That's the best explanation I can think of as to why they never play at the same time. I don't buy the "Pop's a moron" argument or "he doesn't spread the floor" BS.
Although Tim's no longer MVP or all-star level, he's still good enough that Pop can allow Tim to continue to be the guy, at the expense of playing time for Tiago. And because of their loyalty to one another, this will continue to be the case as long as Tim can put up acceptable numbers.