It isn't incompetence, very few people in the world could look at the math and get a proper understanding of what happens. Math isn't meant to be an explanation. Even if perception could be brought down to the level of mere numbers, what would you gain from reading the sums that words couldn't give you?

A quantitative understanding, a tool which you can use to measure the validity of a model, by making explicit numerical predictions and comparing them to reality.

How could you determine which works and which fails without a full understanding?

Not everyone would be able to understand it, but some could. Just because some people can't understand it doesn't mean it isn't real.

Also remember that math is not only numbers, it is also other concepts like geometry.

The math necessary to model reality is never simple.

That depends vastly on what level of accuracy you are going for.

One is measuring the circumference of Earth based upon a distant sun and round Earth vs measuring the height of the sun based upon a near sun and flat Earth.

Both will be limited by the accuracy of measurements and slight issues with refraction, however there is very simple math which can be used.

For a round Earth you use the different in angle to determine how far around Earth you are, and the distance between the 2 points to determine the total circumference.

For a FE you use 1 or 2 right angle triangles and simple trig to determine the height.

This is simple math that almost anyone can understand.

Guess which one matches reality when you have multiple measurement points?

The RE math. It returns a consistent answer.

The FE math fails spectacularly.

Then there are other times where the math to understand reality is complex, but the math to understand a FE is quite simple, such as the bearing to the sun.

Again, FE fails to match reality, while RE matches quite well.

Some more simple math is regarding eclipses, not their timing but their apparence.

In order to have an annular eclipse (which happens in reality), the moon needs to be smaller than the sun.

In order to have a total eclipse which is larger than the moon, the moon needs to be larger than the sun.

In the FE model, the moon and sun are both tiny. roughly 30 miles across if I recall correctly. Yet there are total solar eclipses which are much larger.

Again, this shows the FE model to be false.

This provides a measure between the 2 models which shows RE models match reality while FE models do not. This allows us to rationally conclude that Earth is almost certainly round, and that these FE models are false, i.e. they are not accurate representations of reality.