Leaving aside the law's ups and downs, the only point in City's favour is that the system its owners bought into has always been unfair. But that's true of every regulatory environment: that's why things get regulated.
This gambit is otherwise a vast, incoherent insincerity. City are trying to argue ordinary competition law should allow them to be arbitrarily unprofitable, while also having been the "winningest" club in a competition of which the administrator must retain the power to arbitrarily regulate clubs—necessarily with economic consequences—in order to function.
It stinks of childish arrogance on the part of Mansour and City Group. There is no categorical imperative in action: they want everything their way, forever, and they're happy to destroy or destabilise the league to get it. They don't grasp the perceived (if not real) probity of the league is what legitimates their victories. This undignified legal escalation on ulterior motives detracts embarrassingly from any legitimacy they've had.
On the bright side, this is the kind of existential threat to English football about which Johnson's threat of an independent regulator was raised. The Premier League will have to be very committed to putting City back in their box, so as to avoid losing control itself.