Since the Antiquities Act was passed, over a dozen national monuments have been reduced by a sitting president. For instance, President Dwight Eisenhower reduced the Great Sand Dunes National Monument by 25 percent in 1956, President Harry Truman reduced the Santa Rosa Island National Monument by 49 percent in 1945, and President William Taft reduced the Navajo National Monument by 89 percent in 1912. Elections matter: The policies a president employs reflect the political environment during his tenure.
If a president can establish a monument without an abundance of justification or oversight in the past, it stands to reason that a separate president can diminish and, by that same logic, even rescind that monument, according to his discretion and current conditions.
You can write with a pencil, but you can also erase with it. (The eraser is attached; otherwise the tool is incomplete.) The same principle applies to these executive powers.
The other branches of government have used their own versions of an eraser. Congress regularly enacts new legislation, altering old policies to reflect current preferences and conditions. Even the Supreme Court, which is heavily invested in the principle of precedent, will overrule subsequent holdings when a violation of constitutionality is apparent. The president has the same authority over the executive actions of the office. Checks and balances can run vertically across administrations in addition to horizontally over the three branches of government. We should protect lands of historic, cultural and scientific value – but not at the expense of our hindsight.