Federal courts are restrained by the defining document of this country, and by the other branches of government. This is literally the reason why all power is not vested into one branch: to restrain each other from the known corrosive effect of power.
So no, they are not empowered to do this, and they don't have much power (comparatively) to be shielding from free speech in the first place.
And what restraints are in place on social media or app platforms when they police speech? Only the ones they place on themselves, so this analogy is broken.
So you're saying, if I understand correctly, that private orgs (not anyone), unconstrained from what constraints they are allowed to apply, will eventually include inconvenient speech.
Probably, but as long as the government isn't putting undue constraints on, the market solves this problem. Parler is right there if a person doesn't like Facebook.
This is a hypothesis in want of evidence.