Glad you're not the GM. A big part of managing a team is managing egos. Having Gaudreau for 6 or 7 years, while he hates the team and pines to leave the first chance he gets, is no way to build a winning hockey team.
A contract isn't a bargain if the player hates the team. At that point you've created a toxic environment and you might as well trade him.
The Flames need to figure out how hard they really want to push here. For example, say the numbers are $6.75m vs $7.5m. Those are two different numbers and obviously the Flames want the lower one. But is it worth it if you have to destroy your relationship with the player to get it? Not saying this is the case but other team/player relationships have been destroyed over less. This isn't like negotiating in nhl16. Sometimes it's not worth it to nickel and dime your best player so you can save 1% on the cap.