Hypothetically what you're saying is true. City hypothetically doesn't need to live with their bad decisions. They haven't really made many bad decisions (at least not since Pep arrived, they obviously bought a whole slew of overpriced players in the first few years after the takeover), though, so it's more hypothetical than anything. What you're describing with sacking managers at first sight of poor performances, buying players and replacing them at once is actually a lot closer to how Chelsea have operated over the past 15 years than City. No club in the Premier League has gone through as many players and managers as Chelsea has over the past 15 years. So they have actually been doing exactly what you accuse City of being able to do. The only reason they haven't been able to perform as well on the pitch as City as because they've had much worse upper management (now obviously, City being as well run as they are is part of their cheating). And even so, until Pep's second season Chelsea was just as successful, and even more so than City.
What duds has City really had since the arrival of Pep that they moved on from fast? I'll give you Bravo obviously, Nolito didn't make any mark whatsoever, Danilo as well and then obviously Mendy was a terrible transfers all things considered. Lately Kalvin Phillips hasn't lit the world on fire. But that's about it. The rest of the big transfers has worked out for them, they have all contributed considerably to their success during these years (even someone like Ferran Torres who only was there 18 months clearly did contribute and then sold for a considerable profit).