I don't think he beats out Splitter directly, let alone Splitter and four mid-level prospects. Splitter has a better contract (Tiago will probably make half of what Aldridge will make in 2015-2017) and a better prognosis for success beyond the next two seasons, as Aldridge's injuries are very troublesome even in the short term. For right now, I think you guys might be overestimating the upgrade that Aldridge is to Splitter, or at least the upgrade that Duncan/Aldridge/Diaw/Pendergraph is to Duncan/Splitter/Diaw/Pendergraph. While LA would have been a tougher match-up for Miami due to his offense, Splitter's mobility was essential to even being able to attempt to stay big against the Heat. Splitter's defense the other three series definitely seems more valuable to me than Aldridge's potential offense, as the Spurs scored very well.
As I said, though, the biggest problem I have is the timing. This trade would have looked a lot better to me earlier, as the team would have been able to gear free agency toward replacing Splitter's role as the backup center. Now (or actually after January 15, as that's the earliest Splitter can be traded), there's no real opportunity to do that, and there's even less opportunity to work the pieces in mid-season. I don't think it would raise the team's ceiling unless Baynes or Pendergraph breaks out and proves to be capable to filling Splitter's current role.