In a rebuilding context, White's salary is irrelevant. Definitely, if the Spurs' plan is to hit on a lotto pick that will somehow solidify the DMDR/Gay/LMA core into a contender, then having a solid role-player like White on a cheap deal is great. But if you're talking about core pieces, either White's going to be cheap or he's going to be a building block -- he's not going to be both, not in the long term anyway. A strong role-player just doesn't compare to a legit star. I'd rather be paying a legit star the max than having good-value guys but no stars.
You definitely don't trade Derrick just because, but if the Spurs get up in a position where BPA is a PG and have a team on the phone willing to trade a mid-first for White, I think you make that deal. Hopefully for White, it'd lead to him finding a really good home for the rest of his prime. Then the Spurs could roll with that new guard, Murray, Walker, Mills and Weatherspoon as their smalls and target a defensive four with their other first. Then they can roll out DeRozan, that forward, Aldridge, Gay and Poeltl to fill in their 10-man rotation.