Outside of the PK there's little inherent value in playing "defense" well. Having good defensive skills is a means to an end, the end being controlling the puck and creating scoring chances, and ideally outscoring the opponent. If a player is elite defensively and uses that skill to regain the puck and move it up the ice, the value is in that when that player is on the ice his team has the puck. Not in the way he makes that happen. There doesn't need to be a caveat when Subban or Karlsson win the Norris that they're "not good defensively" (the idea Subban isn't good defensively is hilarious, as is the idea that Karlsson is "bad"). Defensive skill is just that, a skill. It's one tool in the toolbox. Do we need to throw an asterisk on Lidstrom or Karlsson's Norris wins because they didn't hit like Pronger or Chara? Of course not, we recognize that they're different players and were/are elite players based on different skillsets.
All round ability isn't about having a perceived "best" combination of inputs, it's about having the best output. Skating, shooting, passing, hitting, positioning, strength, hands, vision, hockey sense, effort, they're all inputs, and a player combines all of these attributes to create an output of possession, and ideally scoring chances and goals. Hal Gill was one of the slowest skaters in the league and managed to be effective. Karlsson's effectiveness is greatly based on him being perhaps the best skater in the league. Weber and Chara score a lot of goals with a big shot. Subban uses his edges to control the puck like few players can. That doesn't mean a great defenseman needs to be as good a skater as Karlsson, shooter as Weber, or control the puck like Subban. All it means is those players use their skillset to produce elite results. Value the results, not the skillset. Marc-Andre Bergeron was one of the best shooters in the NHL. Douglas Murray was one of the strongest and most physical. They're out of the league now because even a high end tool doesn't mean anything if the rest of your game isn't up to snuff. It's also why Dennis Wideman or Andrei Markov aren't getting Norris discussion even with high point totals, while Mark Giordano and PK Subban are.
The extreme example is Team Canada at the Olympics. They weren't successful because of playing great "defense" (although they'd have been capable at that as well), they were successful because they just flat out dominated possession against everyone to such a degree that they didn't even have to play defense. Even if you're the best defensive defenseman ever, you're still better off if you don't have to defend in the first place. I'm also not sure I buy the idea that Weber's an amazing defensive rock. He's big, Canadian, shot a puck through the net, and has a beard, so it feels like he should be Chris Pronger, but I don't really know if I think that's true. I think he's very good at both ends of the ice but in my opinion the legend of Shea Weber and his defensive prowess is a bit overblown. In my opinion, Subban, Karlsson, and Doughty exist on their own tier separate from Weber. Weber might not even be the best defenseman on his pairing.