About 800 miles apart, from the top of each <(Washington Monument to Gateway Arch St Louis), what can you see and what can't you see of each structure in relation and comparison to FE vs RE? And Why?
Then a shorter distance from the Washington Monument to the WTC New York or any high raise in Ney York
Here's some heights to start with.
https://www.nps.gov/jeff/planyourvisit/arch-height.htm
Earth's shape has nothing to do with your query.
The farthest one could see due to haze and other such issues is around 300 km.
FET claims the moon is 4,828 km from the Earth. RE technology measures the Moon to be 386,242 km from the Earth.
The Sun is blocked by the Moon in eclipse.
Point being you can see much farther than 300 km unless solid objects obscure line of sight.
Sure weather conditions can limit distance of sight but lets say, hypothetical, it's a clear day and you drop a coin in one of the powerful binoculars or telescopes that are available on the the structures mentioned, or you bring your own.
But totallakey, you bring up the question, why is or sight limited to 300 km when looking out across the Earth?