Your take and mine about what’s “right for the team” in this case is polarly opposite.
You are allowed to be wrong.
If one of the first things you do as GM is appease a player who already has bolted on you once and wasn’t training seriously enough then you’re sending quite the wrong message to the team about your tolerance for bullshit right out of the gate. No sir. Not for some dude who has already taken his toys and gone home previously and hasn’t done dick on North American ice. Not on board with that message at all from the perches of NYR leadership.
You may not be on board with it, but when it's that message, or lose the player, you choose the former approach. Even if it's only until you can quietly trade the player.
Then take later steps to rectify the message. Again, if it becomes more of a pattern, the brakes can be applied at literally any time.
Additionally, I don't think that message, if that's the message that even gets sent, which I also dispute, is particularly absorbed by all the hard workers we clearly have here.
Country club message all over again.
I have no interest in having a country club mentality, don't get me wrong. I'm saying making an exception for one player when that player is in the unique position of being able to and having the desire to bolt, is not creating a country club mentality.
You are taking it too far the other way. It doesn't have to be all Ryan Callahans and John Tortorellas here. There is room for a little bit of diva, if it comes with talent and doesn't get out of hand.
This is one guy who has tremendous value either as a player or an asset. Appeasing one guy who acts out doesn't undermine team culture, doesn't create a slippery slope.