https://wiki.tfes.org/The_Conspiracy#Motive_of_the_Conspiracy
Reposting this link to emphasize that this is not tfes conspiracy theory. The conspiracy is in space travel, not on the shape of the earth. NASA still believes the earth is round.
From the above linked page:
At some point, perhaps after the Apollo 1 disaster, it was decided to fake the space program outright and use rockets which only needed to fly into the air until they disappeared from sight.
The earth is portrayed as round in NASA media because NASA thinks it's round. They are not running a real space program, so they wouldn't know what shape the earth truly takes.
This introduces a lot of problems. What was the space shuttle program? Did they launch a shuttle while thousands watched, then it crashed into the ocean, days later to launch an identical shuttle from some remote location so it could land while thousands watched?
Do the commercial space companies also play the same game? For example, when the Bangladesh Telecommunication Regulatory Commission (BTRC) handed over a milti-million dollar TV satellite to SpaceX, does it just fall into the ocean after launch? BTRC then starts communicating with their satellite, who fakes that the satellite is in place? When BTRC points their dishes towards where they think the satellite is, how does it work? I've seen claims that people continuously launch balloons replicating the functionality of satellites, does SpaceX replicate the functions of the satellite in these balloons, thus faking their customer? How could this be profitable for SpaceX? Replicating the functionality of the satellite is non-trivial and maintaining the balloons during the entire life of the satellite is cumbersome, plus it's not in California, they would have to manage this near Bangladesh. I don't see how this could be profitable, reverse engineering someone elses satellite is non trivial. Faking the movement controls of someone elses satellite is non trivial. Replicating the functionality of someone elses satelling is non trivial.
Or, on the other hand, is BTRC in on it as well, they handed over a dummy satellite and they manage the faking of the satellite functionality themselves? Why would they do this, wouldn't it just be easier for them to just launch the balloons without the satellite fanfare? How does this benefit the BTRC? They don't have a vested interest if covering up NASA's coverup.
These issues don't go away with simplistic claims that NASA is just faking it, there are many other entities involved that would have to be enticed to fake it. The scope of the conspiracy grows terribly large.