Anyone who says that FFP was conceived as a conspiracy between UEFA and the big clubs is ignoring the evidence. At its conception Platini made conspicuous references to debt as being the antithesis to financial prudence, rather than a lack of profitability. He would never have made such public utterances had a deal with the established elite already been struck, given how hampered by debt so many of them were, and remain.
What then clearly happened was that sometime after this, either collectively, individually, (or both) words were said, veiled threats were made by the likes of united and Bayern, and FFP morphed into what we see today.
I don't think these changes were to stop City per se, but rather its broader aim was to prevent new money coming into the game to challenge the established order. It is bound to fail imo. Human history teaches us that those with the most money always end up ultimately wielding the most power, no matter how much the prevailing establishment tries to prevent it.
For AC Milan and Ajax read the landed gentry; for City and PSG read Bill Gates and Mark Zuckerberg. The former might have the nicest furniture, but their influence in the modern world is forever dwindling. Cash is King, especially when it's of the black, liquid variety.