That only works if a team has just one midfielder capable of playing that role. That's why it worked with Park against Pirlo, because the other midfielders were Ambrosini and Flamini and neither could damage you on the ball with space. Same for when Klopp did it against Alonso at Madrid since the other CM was Khedira. Against City, you also have Bernardo/KdB, both of whom are great on the ball and can easily damage you if you give them space. Same for Barca with Busquests and Xavi.
That's what makes Rodri such a great player, you don't expect the most defensive midfielder to also be so effective in buildup. Usually a team would ignore the number 6 on the ball and focus on closing space for the other CMs, for City you essentially have 3 CMs who are all great on the ball.