For me the best reason why earth is more likely to be spherical is mostly because spheres are perfectly symetrical on all axis.
With a disc it imply a notion of direction, and asymetry, which would mean some directional force is needed to create it.
As all known forces tend to be factor of distance, it make sense all objects naturally evolve to spheroids as forces are equal at all point at equal distance from a center.
When you put a drop of ink in water, it will more get shaped as spheroids than a cube or a disc.
Even without counting for heliocentric system, it would not make sense that an object stay flat with known forces either it's gravity or magnetism. The force would tend to attract everything at equal distance from a center.
It's even the great misery of mathematician that all is so round, depending PI for calculus, and we still dont know how to compute PI properly.
Beyond this it's not that the heliocentric system is not bogus to a degree, but I dont really see flat earth making lot of sense in itself.
Galaxies still seem to be flats, at least some of them, and all planets orbits are more or less on same plane too, so that could imply directional force somewhere.
Even if i dont really mind in the end if it's flat cubical spherical or donut shaped. And I dont think there is easy way to demonstrate smoking gun proof evidence that it's round like this.
For me anyway gravity alone cant explain exactly how planets got to turn around the sun to begin with, or spiral shape of galaxies, so there is probably some missing forces or missing subtilety additionally to sheer gravity to explain cosmic motion and shapes.
Even all physics law are known to be bogus, they only work at a certain scale, for certain phenomena, it's still all very fragmented as patchwork of different set of equation to use at different scales for different situations.
But I still dont get this whole hate on gravity law, and bogus dodging of one set of equation to replace them with other patchwork of equation that are even more bogus like it's always the trend with this flat earth thing.
You're assuming all "centers" to be single points while in fact most centers are shaped as a disc.
This only move the problem.
Even if centers are discs, it still imply directional force.
Even like tree trunks are round. They are cylindrical because of concept of up/down with sunlights.
But in space, there is no absolute concept of up and down, left / right or such.
Sphere have unique property that they are identical when viewed from any angle.
Unless there is some kind of directional force at play in the universe to give a sense of up/down and direction, there is no reason for anything to become shaped as a disc.
All known forces in Physics are not specially directional. They apply in all direction the same.
Im not sure how flat earther solve the issue that most celestial bodies appears round no matter from which angle they are seen.
That would imply some kind of billboarding like in video game to keep all discs faced toward earth to keep them viewed as round no matter the viewing angle ?
Even if curvature is not seen in picture taken from altitude and planes windows are faked, we still never see a picture of earth with all continents on a single face ?
And we still never see the "side" of it either.
And it always looks the same shape from all angle, no matter which part is visible on the picture. So that would be hard to explain this with disc shaped earth.