Why would they need to do that in the first place...?

That's a controlled-opposition statement. The real cover-up is that the flat earth was intelligently created, meaning God is real, and we are not mutants that emerged from pond scum.

What if the entire "flat-earth" conspiracy is indirect, reverse, subliminal, psychological propaganda being used as deception by satan to get bible believing Christians to waste time talking about conspiracies and "flat-earth" evidence instead of the gospel of Jesus Christ?
Remember that satan is the father of lies and will use someone "trying to prove the truth" to fool themselves into thinking they are "helping" to keep them from sharing the gospel.

Realizing the earth is flat is what made me come back to God and Jesus, because a flat earth had to be created by an intelligent being, and not some random explosion. It led me back to the Gospel. Once I knew the earth was flat, I moved on from that topic and picked up the Bible. So, it didn't keep me from the Gospel, it drove me to it.