No.
He's done great job. Their roster just isn't nearly good enough to compete.
I feel like the roster is more flawed than the coaching.
Not enough forward depth to win a cup.
It’s not lack of depth that’s the issue IMO; it’s the lack of star power. In any event, I agree that the Canes’ problem is one of roster construction. It’s hard to win a cup with a team that’s very good top-to-bottom but is missing those game-breaking talents. The Blues won with a roster like that, but most cup teams have both superstars and depth.
What should they do to get to the next level, though?
Clearly, their strategy of lobbying every puck they can at the opponent's net gives them about eight wins maximum in a playoff year.
I'm not sure firing Rod alone would get that roster any further in the playoffs (the team might very well do worse), but I honestly don't see them winning a Cup with that core and that system, either.