The Lat/Lon system does assume that the earth is a sphere.
Nope. This is more dishonest/ignorant misdirection. Sure, latitudes and longitudes make sense in a spherical coordinate system, but latitudes and longitudes do not affect the underlying metric. If you assert that the Earth is flat and that there is a Cartesian coordinate system that can be slapped onto the Earth, then you will quickly see that the distances don't add up. Simple as that.
There is a valid counterpoint in that because FE asserts that "you can't travel in straight lines" you can't actually reliably measure the distances and all of the discrepancies could be accounted for by measurement bias... Good luck with that one.
The coordinate points in the latitude and longitude system which wraps around the earth are spaced out equidistantly, as if the earth were a sphere. Calculating the distance between any two points would give your the spherical coordinate distance.
It's not really that hard to see that the entire system is based on the idea of a spherical earth. Both latitude and longitude wrap around the earth in 360 degrees. It's a system that assumes a round earth. The points are mapped onto the earth as if it were round.
Pull the line from North pole through subsolar point to Ice Wall.
All places on that line will have solar noon at that same moment.
All places east of the line will have Sun more to the west and lower in the sky.
All places west of the line will have Sun more to the east and lower in the sky.
As Sun circulates above Equator (or anywhere between Tropics) the line will go with it, 15 degrees per hour.
All places on the line at its new positions will have the same situation.
Regardless of the shape of the continents.
Where is globe in that?EDIT: That was the way in which we know this:
If two or more places have solar noon at the same moment, it means they are on the same line drawn from North pole, through subsolar point, to Ice Wall.
Such line we call "meridian".