Interesting theory
You mentioned fouls, not tactical fouls
And I would argue that the majority of their tactical fouls don't occur once the counter occurs, which most people get mad about. The majority of their tactical fouls occur immediately they lose possession, attempting to recover the ball, before the counter is started. The article mentions this.
Plus unlike those advocating for blue cards, I don't automatically view a tactical foul as worse as a foul. That's an artificial differentiation.
A lot of what they do is cynical but it's hard to card, because then you'd have to card almost every foul by any team
"Counter already started, defender steps across attacker without playing the ball"... If that happens, you're getting a card automatically, 99.99% of the time, unless the ref didn't see it. That applies to City, United, other teams...
"Possession is lost, attacker challenges defender with the ball for the ball"... A foul is usually given. And there is a cynicism behind the foul of course, but generally speaking, refs will almost never give the yellow for that, unless excessive force was given.
City used to be great at the first item, with Fernandinho the major culprit. Then the league started cracking down on it, and City's struggles in 2019-20 were partly to them conceding more goals.
Today, they're great at the second option. As soon as they lose possession they use the first wave of pressure (headed by their front men) to try and win possession, even if that behavior may have the foul called. That delays the counter and allows their defensive shape to set, so it is cynical, but it's not as cynical as cutting down a midfielder running at their defense. And there is a desire to win the ball back (at all costs)