All good questions. I don't know him so I can't answer that All I can say is that when you are being paid millions to do a job, you approach it as such. I think sometimes we as fans think that the players see it as more than a job. Yes, they want to win it all, but they also know that statistically it is unlikely. You have a guy like Hank in NY come out and say that even if they rebuild he wants to be a part of it.
The players does not sign any obligation to the team that stipulates he cannot request a trade. There is no such clauses in NHL contracts, as far as I know. What the player commits to are the terms of the contract, and it is understood that the contract is tradable. So if a player doesn't want to stick around for rebuilding years, he can ask for a trade. There is nothing unprofessional about this.
What is unprofessional is Radulov bouncing to Russia because he doesn't want to follow the rules. Or what Spezza did. Or Drouin refusing to go to AHL.
Asking for a trade because you want to be on a competing team rather than a rebuilding one is perfectly fine.
Hank has been in NYC for his entire career and he's about to turn 36, he's been there for 13 years. Once you get at that age, your priorities can start to change as you are nearing the end of your career, and finishing your career where you started is a rarity that can also mean a lot to a person.
Weber has already been traded, he didn't ask to come to Mtl, he isn't from here and has no attachment to this city, and he's 32. He can easily go play for another team for an extra 5 years. Can't say the same about the King.
Anyways, each situation is unique.