It's got nothing at all to do with him appearing lazy, nothing. There is also no stat that says he runs the most, he doesn't. This is what happened, people noticed that Ozil was terrible consistently in the biggest games, largely because he's put under more pressure by better midfielders and better defenders track the players ahead of him better making cute passes much harder to find. AT some point after 6+ months of criticism the entire media suddenly went on this campaign of disproving that Ozil was lazy.... something literally no one was accusing him of. They trotted out stats like how much he ran on average, which is entirely pointless when the criticism was specifically that he disappeared in the big games. If you disappear in 10 out of 50 games a year, a stat covering all 50 proves absolutely nothing. You could run 12km in 40 games a year and 2km in the other 10 and you'd have an average stat of 10km.
Assists also doesn't mean much alone. He takes freekicks and corners, there are numerous games against the biggest and the worst opposition where he'll be dire for 89minutes but take a corner someone else won and we get a goal off it.... but in part because of that terrible performance we lose 5-1. Good players are good for the majority of the 90 minutes in the most important games and even if they don't get an assist, maybe someone else doesn't get an assist himself but we win that game 1-0 in part because of a brilliant performance over 90 minutes.
The best teams have players who perform over 90 minutes consistently, Ozil does not perform in the most important games, he never has. Notice how in summer and jan we got offers from more than one club for Sanchez. We got no offers for Ozil from any top clubs, just the same kind of media interest that managers/agents push out there when trying to get a bigger contract. Why didn't Utd offer 20mil for a guy out of contract just to see if we'd take it?
Ozil was bad today let alone against City in both games where he was absolutely useless, he's been useless in the round of 16 for 3 years and poor in most of our other bigger games.
He's monumentally over rated, he wasn't worth the ~200k a week he was on, he's absolutely not worth the 350k a week he's on now, no one else thought he was worth grabbing at over 250k a week(presumably at least an early offer from Arsenal) so no one bid on him. He's not lazy, lazy isn't the issue, he's a giant girls blouse, he's weak, he doesn't like to fight, he has terrible motivation, he has no fight in him. He cruises around at the best of times against the likes of Brighton but the lack of quality from other sides means he still gets time and space and helps make things happen, but against the big teams his style is shown up as useless and he quickly gives up when things aren't going well for him.
KDB is better than Ozil in every aspect of his game, he's on much less money. In a game City are 4-0 up in, KDB is still making tackles, he's still working hard, he doesn't let people just run past him unopposed because he thinks he's better than that. KDB is the kind of player who would deserve 350k a week, he turns up in the big games, he doesn't give up, he doesn't act like he doesn't have to help the team. He's exactly the guy who shows up for 89 minutes in almost every single game. Ozil is KDB, without the energy, work rate, consistency, motivation, strength or attitude required to be a truly top player.