Facebook abandoning the App Store just to remove the privacy warning labels would be corporate suicide. They'd just be trading one set of scaring warning labels for another (because side loading would certainly have scary labels). And they'd have way less exposure to new customers.

The iOS built in controls would still be the same.

There just isn't a compelling case for a major app to go sideload-only. This entire line of reasoning smells like FUD.

Personally, I would prefer just one App Store with Apple compromising in other ways. Lower fees, consistent application of the rules, and proper support for PWA's. How do you feel about that?