...whose sovereignty is what backs a constitution, which is what courts derive their authority from. Devoid of institutions, 'the people' are no more than a mob, which lacks anything more than a pretense of moral authority.
From the point of view of the minority, that's still all "the State" is: a mob. "majority rule" is just a euphemism for "tyranny of the majority" or "mob rule". And even a representative republic system still can't guarantee that the majority don't violate the rights of the minority.
Let's say you were an innocent man, wrongly convicted of murder by a jury. Would you feel that the State truly was justified in imprisoning you for life or executing you? I mean, the "institution" of a court and judge and a jury decided to do it, so does that make it OK?
Meh... courts have no real intrinsic authority. All political power ultimately derives from the people, and their consent.