I haven't totally settled on the idea of not wanting Aldridge, but I look at it like this:
1. It's not like the Spurs are that bad. In spite of major injury troubles all season, we came within a whisker of a 2 seed in a stacked western conference, and in spite of two starters playing injured we came within a whisker of beating a really good team in the first round.
2. Aldridge is going to cost someone in the neighborhood of 19mm dollars next year. For a Spurs team that is generally built on spreading the money around to lots of good players, it's going to be tough to manage two max contracts plus TP's 13mm. That's 75% of the cap right there, and if you assume that the Spurs hang on to Mills, Anderson, and only one of Diaw and Splitter, that leaves the Spurs just ~4mm under the cap. It's not a hard cap so they can get around that to some extent, but the scenario I just talked about gets you Kawhi, Aldridge, TP, Mills, Anderson, and one of Diaw/Splitter. That's one heck of a top 6, but you've still got to fill out 7 more spots including hopefully re-signing Duncan! Put in 10mm for Duncan (a great value if he plays next year at 75% of what he did this year) and they'll basically have to sign 6 vet min players.
3. The counterpoint to salary issues is that maybe the Spurs need to accept that they'll have to have a couple years of not having the depth to really contend in order to secure the Duncan succession plan. It's a valid argument; the cap is going to go up soon to create more space to fill in some gaps.
4. Of course, the cap is going up for everyone and the Spurs will not be the only team trying to find pieces to put around their stars. There are going to be some REALLY STUPID contracts given out in 2016 and 2017.
5. Also, the Spurs are still really good, and IMO it's better not to get too machiavellian on roster building. If you're already really good, just try to stay good. A lot of people wanted the Spurs to break up the team after 2013, but then we came right back and got a title the next year. Much depends on whether Splitter and Parker can actually be healthy again. Unless the doctors are saying that one or both of those players are flat done, I'd rather try to find a solid second unit playmaker than shell out a lot of money on almost anyone.
6. Looking at Aldridge in particular, his defense is not what I want from a max player. It's not horrible, but it's also not "anchor the defense when Tim Duncan retires" good. OK, that's not a reasonable expectation, but I'm not willing to potentially give up a couple years of contention for a guy who is fairly average at half the game. Offensively I have no problem with his game. He settles for tough fadeaways more often than I'd like, but I also mostly watch him against the Spurs who are good at making that the easy way out.
I don't think the Spurs organization would incur the wrath of point 2 for anything short of Anthony Davis or MAYBE Marc Gasol.