Why are people thinking this is just black and white? Again, I'm going to put on my "mostly baseless speculation" cap for a second. Kawhi could both be injured and want out. If he doesn't trust the Spurs' medical staff and think listening to him will threaten his career, it makes some sense to not play for them again. Whether that's because of issues like with Tiago and Green and Mills (and Kawhi's own history with his ankle injury) or independent of them. The Spurs don't have a tremendous track of dealing with injuries. It's probably not their faults, but I wouldn't know more than people behind the scenes would. One IT-like complication is enough to permanently tank his value. So yes, sitting out could be better for his long-term stock if doing so avoids either a major injury or an extended period of time for other teams to see he's not healthy anymore.
For folks acting like SA would instantly honor a trade request, come the on. They would only move Leonard as a last resort. If one year of Kawhi is supposedly enough for Boston to give up everything they can (it's not, but for argument's sake), then having that penultimate season to try to win with Kawhi has more value than whatever decrease of trade value they can expect (ignoring all the reasons why it'd be better to wait, as I've been saying). They wouldn't entertain trading him until he rejected a contract. He could be jumping up and down right now for a deal (funny considering the injury), and they'd still hold him, hoping against hope he comes back to the court for another dark-horse run to a le. You can always blow it up, but once you do, you can't go back.
I still think the most likely way this plays out is Kawhi signing an extension and either staying long term or being traded in 2019. Kawhi has his cake and eats it too. The team gets a chance at a le run. Kawhi's future team (if not SA) gets him on a long-term deal. Win/win/win(?) for everyone. I don't think we've seen the last of Kawhi as a Spur, but there's not much else to talk about right now other than off-season scenarios, so what can you do?