And there'd be no point for Minny to it without getting a top piece. They aren't going to move Brodin for secondary pieces.
Plus, Rask is solely a buy-out candidate/AHL depth to Montreal. He's not supplanting Danault or Domi, each of Kotkaniemi, Poehling and Suzuki will see/likely need to see reps at center in the NHL now or in the not to distant future, and Thompson (and possibly Evans in the AHL) fit a 4th line C role at a better cost point.
Rask can at least serve a role for other teams (or even the Wild), he's entirely unnecessary for Montreal.
I don't think anyone wants Rask as a $4M fourth-liner. That greatly narrows the options to teams who intend on taking his contract and burying him or cutting him. So I think that actually favours Montreal, who as you said, won't even play him. But they have cap just sitting there, so why not?
This is like how they landed Armia. They took Mason to get him.
My feeling is that Brodin is a deadline trade candidate next season so I think Montreal would be willing to pay that price right now, but by taking Rask, they can subsidize it a bit. Maybe Minny doesn't want to dilute the Brodin return with Rask though.
If I were the Wild, I would just stand pat but the whole premise of the thread is that they want to shed contracts. All their big deals are tied to recapture and the worst contract after that seems to be Rask. As many have said, why attach a young player to a contract? They might end up trading Brodin anyways, so i think Montreal would be in on that right now.
I don't know how they feel about Staal but you could even take Rask and Staal in a Brodin deal. Staal can take Thompson's place on the 4th line.
They can throw in Pateryn instead of Staal if they want.