I haven't thought about it cos I've never figured on the Spurs spending a lot for an unsubstantiated quality; it's never been their style. Even with Kawhi forcing their hand, I think they're very much in wait and see mode.
For the Kings to do it, they'd want to have Kawhi sign the extension and commit to them in advance, imo. If Kawhi is that serious about getting closer to LA over competing, then yea it's possible. But I don't think he'd settle for that. If it were to be done, it'd have to be in a three team deal with LA or someone like Boston who might take their chances on resigning Kawhi while competing for a ring. Also, the Clippers who have the 12 and 13 picks could be a player instead of the Lakers in a multi-team trade scenario.