Couldn't think of a better title than this. Aristotle said that "It is the mark of an educated mind to be able to entertain a thought without accepting it." F. Scott Fitzgerald famously wrote: “The test of a first-rate intelligence is the ability to hold two opposing ideas in mind at the same time and still retain the ability to function. With love I will share some of my beliefs. God bless you all.
I am not a flat earther, but I do respect them. You know you will absolutely be ridiculed, yet your brave enough to share what you believe to be true. While I don't think the earth is flat, I do think that the level of deception pulled on us all is so great that the world might as well be flat. Meaning, our lives are built upon so many lies, that the earth being flat would be no crazier than the contrast between the lies most of us believe and actual reality.
I like the quotes about being able to hold all possibilities in equal respect. In math there are several ways to define space. We have Cartesian space (x,y,z). We have polar space which is like we measure our position on the globe. There are several different spaces to do math in but the general idea is that each interpretation is valid and can be translated to other spaces often with no lost information. I can see in thought how each space can be useful for different purposes. If I want to conceptualize moving around my city on a map it doesn't do me much good to view the world as a sphere. However if I want to travel long distances a spherical based space will help me conceptualize my course. I can see how the flat earth model and spherical earth model can be used to understand the natural world. It could be one or the other, neither or both and it makes no difference to me for most intents and purposes. Have we examined all of the possibilities? Is it possible that the earth may be an even different shape?
I have no definite opinion to the shape of the earth. I would like to point out that the examples you posed are referring to flat earth as a basis for a modeling a motion from a reference point. It in my opinion that this only speaks to the assumptions made to form their models and has no definite dependence on the actual shape of the earth. I think reality shows both models to be flawed in that certain phenomenon have no discernable cause. One mathematical quandary I have noticed with spherical earth is the great circle problem. Imagine you are on the north pole. Now if you travel in any direction in a straight line (on a great circle) you will travel through the south pole and cross the equator twice. Now take a similar trip starting from your current location. Regardless of the direction you begin in you will pass the point opposite on the globe and cross the equator twice according to spherical geometry. According to reality it seems to me that if I walked say due west that my latitude will not change as spherical geometry would predict. I have no idea how to test it but I seeit as something that presents an issue with the sphere idea.