Regarding your 'real world' flight path, I'm not sure how accurate that flight path actually is. It is a representation of the "shortest apparent distance," sure, but it is not a path that a flight will necessarily take. Flight paths generally run along the jet stream or with tailwinds, so they change. These images show the differing flight paths from Dubai to Sao Paolo at different times of year - the flight paths change based not upon distance, but wind.


Those are four widely varying paths, none of which take the apparent shortest route. These flight paths have less to do with the shape of the earth and more to do with the weather conditions and winds. The "May" route comes closest, thanks to coincidentally favorable winds. Aircraft routes are not proof of the earth's shape, spheroid or plane.