Halak did not want to be here enough to invest money in him. The flap with him punking out AND his agent yapping about it in the PRESS was enough to piss off ownership and show them this guy is not committed to DC and is ripe for issues. Whatever sentiments about money or other factors from Halak's end that came out after that would only add to the strikes against keeping him as far as the Caps management would be concerned, imo.
This team just cleaned out their GM of 17 years and a coach with another year on his contract. They are not going to pony up big money for a UFA rented by the previous GM, especially with all the issues involved, and with a cheaper goalie that's been with the team for years who's potentially as good or better already on the roster. Even with Oates ****ing with him, Holtby had some great moments and put up numbers close to Halak's. And when you compare career playoff numbers they're very similar, with a slight edge to Holtby, iirc.
You are also not going to pay Halak twice as much as Holtby to be a backup, so if you're keeping him you have to deal with the loyalty issues and make him a starter because he isn't taking less money than Holtby. The fact that a team traded a pick for negotiation rights indicates there's probably at least a few interested bidders out there so he wouldn't be cheap, if he'd even want to stay. Then you're throwing 4 or 5 million of your cap space at a starter with questionable motivation who may not be significantly better than your $2M guy, whose development arc will again be put on hold or moved farther backwards.
Caps were a motivated seller here. Getting ANYTHING for Halak is a win. A new GM will have discussions with ownership about direction coming in, so it's likely they would've communicated their opinion on Halak to him just as they would Ovechkin or any other player whose role they believe to be mostly settled. I wouldn't expect a newly hired GM to walk in and trade Ovechkin right away, and I wouldn't expect him to show up and quickly throw a bunch of money at Halak, either.