It's nice to support a team with competent leadership and that knows what it's doing. Hands go up!
David Poile is one of the best GMs in any sport and made a living on doing the most with the least for many years. In more recent years, he's made moves to get some established players (Subban, Johansen, Neal, etc.) but Nashville has always lacked star power. That doesn't matter. They draft and develop at least just as good as anybody else in the league, but are a small market team. He is such an incredibly shrewd GM, whether it be via the draft, contracts, and trades. I'm still not quite sure how he pulled the Erat for Forsberg trade off a few years ago.
It's also mind-blowing that they came into the league as an expansion team and have had exactly one GM and just two different head coaches. That is insane.
Also, I wonder if the fact that Nashville isn't a hockey fishbowl lends to the team's success. Look at how a guy like P.K. Subban is thought of in Nashville versus Montreal. Montreal is just expected to be elite every year, and there is immense pressure to do so. When an uber-talented player like Subban is expected to carry the team, can't quite take them to the promised land, and doesn't "play the game the right way," he's run off along with the coaching staff. I was in Montreal for work during the NHL playoffs and found that the fans there have a very ambivalent feeling towards him. In Nashville, where a good hockey team is a nice thing to have as opposed to a demand placed on the team by the fans, he's embraced. Just like college football coaches, there are a lot of guys just more comfortable playing in certain places.