What if Congress passes something akin to Buttigieg's plan, which establishes that at least some of the new justices must be unanimously approved by the sitting justices? Can they strike that down on the grounds that it interferes too much with the independence of the Court by compelling justices to confirm new ones?
First off, any attempt to retroactively apply such a rule would clearly be unconstitutional.
But if struck down in total, it wouldn't be because of interference in Court independence, it would be because it would be an unconstitutional delegation of power to the Court, much as how in Marbury, the Court found it was unconstitutional to give the Court the power to issue writs of mandamus.