[NotPractical]

Antitrust law applies to any company of massive size that engages in anticompetitive conduct, not just companies who create "open platforms" [1], otherwise there would never be any antitrust cases. An antitrust case would be your best hope under current law, but it already happened and the remedies did not include a mandate to keep allowing unrestricted sideloading indefinitely.

Anyway, you're now moving the goalpost, because you were originally talking about a case based on the premise that they engaged in fraudulent marketing, not a case based on the premise that they currently hold a monopoly. The former would never hold up in court, the latter already happened but the remedies were insufficient to stop Developer Verification.

[1] The reason Apple wasn't forced to allow third party app stores as a result of Epic Games v. Apple was not because iOS is a "closed platform"; they simply weren't found to be a monopoly in the "mobile gaming transactions" market (which does not preclude them from eventually being found a monopoly in the "mobile app distribution" market).

See also:

https://en.wikipedia.org/wiki/Epic_Games_v._Apple

https://en.wikipedia.org/wiki/Epic_Games_v._Google

https://www.theverge.com/24003500/epic-v-google-loss-apple-w...