Not even bloated, if you look at PSG, in theory they have a huge market but bad ownership led to poor marketing exploitation. FFP allows QSI to sponsor the club based on its theoretical market and exposure, what they can't do is surpass that theoretical threshold.
And you are right about the rest, the real story about FFP is that it was initially exclusively intended to avoid cases like Zaragoza, Parma, Strasbourg, Le Mans, Portsmouth or Leeds. The initial plan included the use of an administration comparable to the DNCG in France and on top of some of the tools currently used by the FFP. But some FAs were against it and some big clubs lobbied for an anti-City plan instead. IIRC Real Madrid and United don't give a damn about FFP and never pushed for it, it's the other usual suspects.