^^ True generally.
Where are you located, most likely the US ?
Pretty sure in the US (like here in Australia) many local city managers can introduce laws to stop take off and landing on their managed land.
Maybe check local city bylaws if you can fly in the park etc anyway, you might not have any restrictions, and be able to fly close to take off point (much safer !!) to keep an eye on your bird AND people that may come along.
Yes if you take off from private property or other non local authority land, then you should be able to legally fly over the monument, as long as you can still keep VLOS, not over people, and other such FAA rules.
If you do this, plan it for a very quiet time, early morning (with good light / sunrise colours) or during a work day if it's less busy.
Maybe have a spotter near the target, but then you need comms (small 2 way etc) . . . check, not sure if spotter comms are allowable, maybe they need to be near you anyway.