Well despite his flashy "simple stats," Wiggins play has not been contributing to winning all that much. Cousins on the other hand is elite in this category.
I have a hard time seeing how KAT prevents them from wanting Cousins. Both can faceup, both can score in the post, both can knock down 3s at a high rate, both can pass, both can handle the ball, both can rebound, and both can protect the rim & defend. They would rival the best frontcourt the NBA has ever seen. How are teams going to stop Cousins & Towns defensively? If you don't have two excellent defenders at PF & C with size & athleticism, you are essentially screwed (and you still might be screwed even if a team has these excellent defenders). And the fact that both are shooting north of 35% from 3 suggests that both could provide great spacing for one another. They would literally be the anti smallball and actually be able to punish smallball lineups way more than Randolph & Gasol ever could. Not to mention they'd still have LaVine & Bogdanovic as knock down shooters on the wings (and LaVine continues to flash great potential as another threat on the perimeter). They'd also still have Rubio as a solid PG & a lot of cap space next year to go out and sign a guy like Porter or Hayward as the SF of the future. Rubio, LaVine, Porter/Hayward, Towns, & Cousins would be pretty darn talented & formidable.
Lastly, Minnesota has Thibs who Cousins thoroughly respects based off his time in international play. It would be hard to see Cousins clashing with him considering Cousins tends to align with defense first coaches. Considering the talent level & the coach, I would think Minnesota would be fairly confident in their efforts to resign him.
EDIT: Thinking about it some more, how would that duo stack up against Golden State? Will Draymond, Durant, & Pachulia be able to contain them without picking up fouls? Or will they have to result to double & triple teams with shooters around them to knock down the open shots. Would the Spurs bigs (Aldridge, Gasol, & Dedmon) be able to stop them without fouling? I don't think so. Would Love & T. Thompson be able to stop them? Again, highly unlikely. Getting these small lineups into foul trouble is there key to takeaway the advantage a Durant would have when Towns is guarding him (for example) on the other end. Getting the other team in foul trouble will not only be their meal ticket, but it will also muck up the game for these chucking teams. It's hard to get in a rhythm if the other team continues to stop the game and shoot free throws.