Very good point.
The 1892 Gleason map, which is sort of the unofficial popular FE map, is a Polar Azimuthal Equidistant (PAE) projection; that is to say, it is centered on the North Pole (there is PAE that is centered on the South Pole, and non-polar AE maps that can be centered on any spot - for example, popular with radio hobbyists to show the direction and distance from their centered hometowns), and shows the distance from the center point to any one other place (but not between two spots if neither is the center point) and the direction from that center point. It is a projection because it is a flat representation of what is accepted by the cartographer as a round earth. This particular projection (non-polar) is used with States and countries but usually not the world (altho it is on the UN flag) or entire continents because of the severe distortion at a great distance from the center point (in this case, Antarctica). Since 1892, when Gleason produced this version of the PAE, there has been some slight improvement; for example, more recent exploration mapped and measured a different coast for Greenland.
But, and this is important, we know that, unlike the Gleason map (or any PAE), Antarctica cannot be the rim of the flat planet. Every year ocean liners make cruises circumnavigating Antarctica, letting passengers off at various spot to annoy the penguins, and if a boat can go around Antarctica then it follows that Antarctica cannot go around the rim of the Earth.
So where is the Rim, the Edge, the Dropping-off line, the territory beyond known geography, and the sides of the flat planet (or the unknown flat territory that some think stretches on and on? It ought to be in every direction, if you go far enough, but nobody's found it in more than 3000 years of human history. Even with jet planes and rockets, nobody's detected this Edge anywhere.
And you know that if this Edge were discovered there'd spring up entirely new sciences and industries - not just in the US but in many countries - to explore and exploit whatever is on the sides of the flat planet. Such a discovery would guarantee an economic and scientific boost to all humanity. So why, really, are all the governments of all the countries, for the past several centuries, denying that the Earth is flat? It certainly wasn't to create a federal agency in 1958 that would simply steal American taxpayers' money, Not even North Korea or Albania claimed that the Earth was not round.