well here's the thing. Monuments are not normal executive orders. Monuments are created as part of carrying out the duties assigned by Congress to the president under the Antiquities Act. Presidential monuments have the same force of law as those monuments created by Congress. This isn't an order directing , say, the Treasury, to come up with a new design for a $10 bill.Such a directive can be undone by the next president.

 Further the Antiquities Act has no provision providing for a president to undo a monument once created. The Forest Reserve Act, which was a law passed in the 1890s allowing the president to create forest reserves, also gave the president the ability to shrink or revoke the reserves.  There is no such language in the  Antiquities Act and 2 Attorney Generals have concluded the president lacks any authority to shrink monuments or undo them, that is solely the province of Congress.