If the round earth is so staggeringly apparent, why did it need to be "proven"? Why do people instinctively know the earth is flat?
It had to be "proven" because ancient flat-earth beliefs, unlike modern FET, fit with observations made in the parts of the world they came from. The sun moved under the earth at night, and the sky was a dome, both things that people "instinctively" know, to use your terminology.
There would be no reason to think the earth was curved because their flat-earth models fit for the smaller worlds they lived in, unless you happened to voyage a lot on water and noticed ships appearing to sink, or noticed shadows of differing lengths at the same time of day when moving north and south, etc.
We're much more aware of the rest of the world now, so FET has had to become a joke to fit with what we know.