Like you mentioned, other clubs such as Bayern, also I'd add Madrid have been able to keep their wages reasonable despite having different managers.
Pep will be gone from City one day, I don't think their wage bill will just skyrocket afterwards and they lose control. If the management does things right like City, Bayern, Madrid and practically everybody else except us, United and PSG (aka the three loonies), it can happen.
Of course, every club has a slightly different approach. For Bayern, they have a firm grip on the region there. Poland, Germany, the central Europe and Northern part is very keen on Bayern Munich, they are like the biggest club in the region.
Madrid is kind of self explanatory, it's a honor to play for that club, and they do not hesitate at all to position the club first. They actually sold one of their greatest player ever arguably without flinching when he asked for more money, the message was clear and decisive. Barca are a sentimentalist club by comparison. They are weak-minded in relation to their best players and their legends, and that is why the club is easily taken advantage of.