It doesn't have to be Portland. All that has to happen is Aldridge has to tell Pop it's time for a trade. Pop was willing to fight it when the Spurs were contenders. I doubt he would be now.
The Spurs are pretty meh on re-signing their RFAs. I'm sure they like Poe and intend to keep him. But I also think it'd be easy to see a scenario where he doesn't come back. He should get a decent contract, and the Spurs may well want to prioritize adding someone to the Murray/DeRozan/Aldridge trio. I also don't think Murray is a lock to come back for similar reasons. Having Milutinov or another rotation-caliber C on the team already would only reduce the chances of Jakob being a Spurs past next season.
The Spurs need Gay, but I also think they have a limit on what they're willing to pay him next season. He's shown his limits in the Spurs' system, and he seems on the edge of even more decline. They may want him on a one-year deal, but they've structured their contracts so that they can have a window for cap space coming up, and I don't think they'll let Gay disrupt that. For Rudy's part, he has to think if winning a le is important to him. If it is, I think he'll have suitors who are stronger contenders. He's already shown he can be a valuable role-player. If the Spurs don't back up the truck for Rudy, I think it's even odds that he's in GS or Houston next year.
I agree it's not hard to find a rotation-caliber center. But that doesn't make drafting one a bad idea. I also think Pop is hesitating on playing more two-big lineups because he lacks another legit big (Motiejunas doesn't count). While I think he would always like the ability to run units with LMA at the five for a change of pace and to match up when necessary, I also think he likes the defensive potential of two-big units. Getting a mobile big like Clarke or bigs with range like Goga or Bol help make that work. Those are guys who should be able to play with Aldridge, Poeltl, Milutinov, Gay or whomever if given some time to develop. Not every NBA team is committed to playing small. If anything, I'd say that the league has started to trend back toward sanity this season.
I don't see why he can't play with a big like Aldridge. He is a rim-runner/shot-blocker like Poeltl. If Jakob and LMA can play together then it's not too hard to imagine Clarke getting minutes in a similar role. It takes chemistry more than anything. Yes, the Spurs would have to be confident in Clarke's potential to shoot from distance. But if they are, then they are drafting a combo-forward, not a center. That position is not remotely easy to fill nowadays. Physically, Clarke can play that role. Skill-wise he can do it on defense. Getting the offense to catch up would make him easily BPA at 18-20. Dude was a top-five player this year. No one projected outside the top-10 can say that.