The idea that the earth was somehow a perfect Cartesian plane could not have existed before Rene Descartes (1596-1650). So the oft repeated idea that everyone before Galileo (1564-1642) thought the world was flat is absurd.
You are correct that, if the world was a Cartesian plane--an idea that post-dates Galileo--then the world would be really strange.
It is interesting that you mentioned gravity. If one had a situation where a mysterious force that pulled matter toward the center of the sphere, aka the center of gravity, then the surface of the sphere would have properties associated with flatness.
Unfortunately, there are people who want to create a conflict where there isn't a need for conflict. Sadly, there are also people on this sphere who want to take any contrived conflict on this sphere to generate contention.