I would do it, but Batherson has neutral or negative value at this point. He went from being on one of the best contracts in the league after his great 2022 season, to being another one of those players who isn't bad like a traditional David Clarkson type contract, but might be difficult to move because of their term and inconsistent play.
Reilly Smith with 2 years left going for a 3rd is a good reality-check with Batherson.
Brannstrom doesn't make sense in the trade, because I doubt Calgary would want him, and he is apparently hurt for a while. Brannstrom would only make sense in a Batherson for Weegar type swap, because they need someone in there to help equalize the cap in/out. Batherson and Andersson already have close to offsetting cap hits.
I think Batherson is the next Zibanejad in that he will probably be traded after being so up and down here, and he will put it together somewhere else. With that said, I don't think on his own he currently has the kind of value needed to get a top pairing RHD on a great contract. I guess it is possible Calgary or any individual team could really like Batherson, but I think it is more likely the trade would be like sure we will take Batherson to make the cap work, but you still have to give us a 1st++.