Public transportation in the US is a long and disappointing subject unto itself, so I will leave it alone beyond simply saying there isn't enough of it.
Large parks were deliberately located a healthy distance away from cities for specific economic reasons. Some good, some bad. Land acquisition costs, balancing between sparse vs. expensive local labor markets, avoiding overabundant development restrictions, seeking pliable and welcoming local lawmakers. The list goes on.
[Edit to add: Even SFA's location used to be considered the outskirts of metro DC. The Capital Center and expanding DC suburbs quickly assimilated the area.]
Also... the fact that these family-oriented parks were largely reachable only by motor vehicle and required single-price admission payment at the front gate meant certain would-be guests would find it harder to get there and come in. This was a major marketing consideration at a time when living memory dictated amusement parks were essentially seedy family-unfriendly hangouts for shady characters, as many trolley parks closer to cities had come to be known. It also was a very convenient means to keep away people who didn't fit a certain economically dominant demographic, sorry to say.