"Clutchness" is in most cases largely just a post-occurrence rationalization of how things happen to play out, and not an inherent quality of an individual. They've also had plenty of clutch moments and putting the team on their back moments. They just get forgotten when the team doesn't win the series.
Except it doesn't. We've had a really balanced team in offense and defense for years, and while goaltending hasn't always been there, we've had pretty average spending on our goaltending, and goaltending isn't something you can just throw money at to fix.
Yes, our defense has been good enough to win, and we have had 4 legitimate top 4 defensemen. Whether we have that now depends on if/how Klingberg rebounds, and Liljegren's development, but that's more a result of Treliving making a questionable signing decision and transferring more money from defense to forward than ever before, not an inability to get that due to cap space.
We've had an effective shutdown line and a pretty quality bottom six for years. Our lack of "shutdown line" now was a decision - opting for players like Reaves that suck and fit nowhere, getting bad defensive forwards, and loading up our top six - not a necessity due to cap. Teams don't really win off high paid bottom sixes. They usually win off filling those spots with cheap players and ELCs that perform beyond their pay.