You picked a bad example in Minnesota. They live and die by high percentage chances — suppressing them better than any team and going for them exclusively at the other end.
That said, you're right that in 2018 it hardly matters if you accumulate shots from way out. I've also always been skeptical of 'traffic' as something that does much of anything except occasionally gets a low-chance shot to go in.
Quinn to his credit has talked the language you're preaching for. 'Going through players' etc. Watching, it's hard to tell whether we don't have the right personnel for the attack you describe. Look around the league and it's exactly that that brings success. Drives to the middle with layers of support. Same with pinches at the blueline. Support not being (exclusively) a player that swings high to cover up ice like a secondary in football, support being players who follow the play closely to keep possession. People focus on this with net-front battles or on the boards, but those small ice battles are happening more and more regularly in open-ice.
Kreider is a great example of a player with the right tools to attack the way you describe. Same with Buchnevich and Zibanejad. As a line, they're hardly scary when they're skating laps around the offensive zone, which they do much more frequently. Circle the zone, feed the point, crash the net, leave the zone, change. If they were stopping on pucks, driving the center of the ice, and supporting one another closely, they'd be a very capable first line.
It's frustrating that we don't do this. San Jose has been sharing this problem, and they're off to a terrible start for it. They have the excuse of wanting to defer to their talent at the blueline, but it's not working that way. Montreal is a good example of doing it well without the talent of better teams.
I am still not at all sold that Quinn really is pushing for the right things.
A typical example that is a good litmus test on whether you are on the right track, if you see this its
not a good indication:
*Zib carries the puck through center ice and gains the offensive blueline with speed pushing the Ds back a little bit
*Zib finds Fast to his right, then drives to the net hard to open up more space and tying up a D
*Kreider does the same thing
*Fast puts a hard low shot on the net looking for a rebound
*The shot is saved and poked into the corner by a Caps D
*Ziba and Kreider are going hard forward and one of them gets first to the puck in the corner
*They pass the puck back to a D who puts it on net again with our 3 forwards going to the net
*The puck is caught in traffic and one of our forwards takes another whack at it
*The puck is cleared out to the neutral zone, the opponent is a little tired and takes a shift and so do we meaning that we slowed them down a bit and didn't lose all momentum
Three shot attempts, it ends with you in a pretty good spot. But you could surgically remove 9/10s of the brain of any NHL D or goalie or center and they would still exactly how to handle these plays. Sure, a shot could be deflected, we could get a rebound, but it will happen 1/20 shots, not 1/10. Against a great D, maybe its 1/30...
A typical example that is a good litmus test on whether you are on the right track, if you see this
it is a good indication of a team that will be very hard to contain defensively:
*Zib carries the puck through center ice and gains the offensive blueline with speed pushing the Ds back a little bit
*Zib havs seen Mario slip two defenders in the 91' cup final to score a goal and tries to do the same thing
*He barely get by one defender but is knocked to the ice by the other, they get tangled up and the D goes down too
*Just trailing him, Jesper Fast is coming into the situation and manage to pick up the puck and tries to go around the bodies lying in front of him
*The other Cap D manage to get a stick on stick with Fast and the puck goes to the outside, Fast and the Cap defender is tangled up and both goes to the ice
*Shattenkirk have joined the play and picks the puck and goes around the net
*He puts the puck on the net where Kreider is standing
*Frederik Claesson have joined the play too and the Cap defenders, both of them just having been forced to scramble to make defensive plays failed to pick him up, as did their center and wingers
If we look at the top scorers in this league, the names that really stand out are guys like Jonathan Marchessault, Brayden Point, Seb Aho, Marchand and Pasternak are exceeding all expectations, Troschek and so forth and so forth -- why is that? Why are these guys so effective in this league right now? Its because they play like the later example for sure. They
genuinely challenges the defenders, they don't skate into the zone with zero intent to try to beat their guy, they go at it. Scoring has gone up a lot, defenders are struggling, this is the big difference.
Under Quinn so far I see a a lot of simplistic school book plays designed to get pucks on net and don't risk too much. Going through your guy seems to be more of a message to the guys going up against a D to get to a rebound. It worked for LAK but the game have changed. We are getting a lot of pucks to the net and shot attempts, but its not going to be effective.
OTOH, every time you really go for it, you risk losing the puck instantly and seeing a counter attack going the other way that surely will result in shots against pressure on the Ds and forwards.