Why are we bothering with a Constitution, then? Let's just have a direct democracy and be done with it.
All I know is that such granting of privileges does not violate the 14th amendment.
To extend the analogy a bit, the problem doesn't lie in the fact that Judge Moore has a nice dacha on the Black Sea, the problem is in his declaration that he's the only one who will have a nice dacha on the Black Sea...
That comes entirely down to who owns the Black Sea and its frontage. If it's Alabama government property, and the people of that state have decided that one of the privileges of the Chief Justice position is to have a dacha on the Black Sea, and yes, other people are excluded, that does not violate the Constitution.
If it's private property, then that's obviously a different matter altogether.