I'm not convinced other teams are beating us at playing fast - they are certainly beating us, but I'm not actually sure if there's anywhere to get team time of possession stats to show that other teams are playing faster on us (as opposed to us playing faster on them) than they do in general.
I look at that as a simple extrapolation from the following pieces of data:
(1) The Kings are first in the league in pace
(2) The Kings are first in the league at FGM per game while being worst in the league at opp FGM per game
(3) The Kings are 17th in 3PM per game while their opponents are 1st in the league in 3PM per game
(4) The Kings have a 24-34 record
So the Kings play the fastest of all NBA teams and score the most baskets per game but allow their opponents to score slightly more baskets, a higher percentage of which are 3's which is a large part of why they are losing more games than they win. It's an oversimplification but the Kings aren't losing the free throw battle or the rebounding battle based on statistics. To me the numbers say they are trying to play faster than other teams but that has not produced positive results.
Outside of stats, what I see when I watch this Kings team is a squad that responds to giving up an easy basket not by getting upset or making any adjustments but by simply running down the court in an effort to "make it up" on the other end. I see a team that is focused on pushing the ball but which struggles to execute in a half court set. And that becomes an issue when the game gets tight and opponents starting picking guys up earlier and earlier - it hurts the ability to score in transition and forces teams to execute in the half court. To me that's a key reason why the Kings rarely "win" the ends of quarters, halves or games. Things tighten up and while the coaching staff may believe "It’s always time to break. There is never not a time to break", that's not quite true when the opponent pressures you enough to force you to slow down.
We're 21st in the league in three-point rate, so it's clear that we're not actually shooting a ton of threes relative to the league - to the extent that Karl's offense calls for us to shoot a ton of threes, we're not executing it.
This speaks directly to the mismatch of scheme and roster. An offense dedicated to always moving quickly, and dedicated to either getting a three or attacking the basket doesn't work nearly as well when your starting PG is a historically bad shooter, your starting (?) SG is a reluctant shooter and your backup SG is having a historically bad shooting year. It also doesn't work as well when neither of your SGs is adept at attacking the basket - McLemore because of his weak handle and Belinelli because of his slow foot speed.
The speed that the Kings play at gives them opportunities for transition hoops at the basket as well as transition/early offense looks from 3 but it also tends to allow them on the other end which is a losing proposition for a poor three point shooting team.
I'd like to see more Cousins in the post, but does he set up outside because Karl wants him outside, or does he set up outside because he's usually the last player up the floor? I'd note that when he IS the first player down, he usually gets into the paint, gets a seal, and we often get him the ball for an easy two.
When running Dribble Drive concepts Cousins assumes the role of the 4 man with Acy, WCS or Koufos acting as the 5 man. In that role he sets up outside the three point line and is asked to shoot from three or attack the basket just like the 1, 2 and 3 man.
As far as the defense goes, I'm not really seeing the pseudo-zone you describe, but I'm not the greatest analyst so I could be missing it. What I do see is a ton of switches - mostly unnecessary - that lead to reliable mismatches for the other team.
At times they'll switch between a modified 3-2 alignment and man-to-man. You can see it when an opponent cuts from the high arc and cuts across to the opposite corner. Sometimes that man is simply allowed to make that move with the down man hedging over to prevent an easy basket but then passing him off to the defender on the other side.
If I were to guess I'd say they employ this sort of scheme because it keeps everyone focused on the ball and ready to attack the other end. I honestly think that's a big part of the strategy.
And honestly I have no idea what the hell the Kings are trying to do against the pick and roll. They don't force them, they don't hedge, they don't trap and they don't really even do traditional zone or switch. The reason the pick and roll is such a big part of most teams' offense is that the defense has to give up something to take away the other options. In general what you'll live with is the pop from the big. But the Kings seem to allow the ballhandler to not only get into the lane easily, they switch to create a matchup with the roll man. I honestly wish I knew what the concept is supposed to be because to me it makes no sense.
It doesn't help that Karl's offense uses almost no pick and rolls in basic sets since that means less reps defending it in practice. Practices that by most accounts were nearly all offensively focused until right around the all star break.
I also see a bunch of three-guard lineups that leave us smaller than the opponent. Is that because of "pace" considerations or because Collison is by far our best bench player?
Personally I'd argue that Casspi is the Kings best bench player. In terms of needed impact I think you can argue that Cauley-Stein is as useful off the bench as Collison. But DC is the best scorer off the bench. I could even side with Karl going to small ball if there was a full sized SF because the Kings SG have been so bad. But I think the three guard thing just stems from Karl's desire to have two ballhandlers on the court, something he's been fond of for years and years now.
Bottom line, I think there are a lot of things wrong with this team (a lot more than I've mentioned above) but to me most of them seem to be unrelated to pace of play or only related through some difficult contortions. And it's not like I'm a big "pace" guy - I want our offense to get good shots, with passing, cutting, getting open...and yes, getting out in transition when possible and taking high efficiency shots (e.g. corner threes). I don't want us to take a fast shot unless it's a good shot, and if we could slow it down and put on a Spurs-style offensive clinic (I don't think we can, but that's another story) I'd be all for it. But I just don't think there's very much evidence that "pace" is the source of all or even most of our ills, and it tires me to see that sort of misplaced blame over and over.
Here's what initially set off alarms in my head about the speed at which the Kings offense was moving. Rondo stated publicly months ago that he and Cousins went to Karl to plead with him to slow things down. The team's best player and the starting PG didn't want to play at the pace that Karl wanted. That's a huge red flag to me. It makes me think that if Karl were the Grizzlies coach to start the year he'd have them moving at the fastest pace in the NBA for better or for (likely) worse.
I don't care what speed a team plays at if it's the right style. I loved the Showtime Lakers, the Warriors are incredible and I hated Fratello's Cavs with the walk it up, plays called out every possession offense. It doesn't matter to me what speed the team plays at as long as it's the one that maximizes the personnel. And that's my issue here. I think what Karl is trying to do detracts from his best players strengths and exacerbates their weaknesses.