If you actually look at real flight paths they do end being straight lines on a flat earth map.
Really? I know that in the Southern Hemisphere that certainly do not.
I have plotted the shortest distance from Sydney, Australia to Santiago, Chile on "Gleason's" map (the same projection as the "Ice-Wall" map) and on Google Earth.
Shortest Sydney to Santiago on "Gleason Map", about 25,400 km | Great Circle Sydney to Santiago on "Google Earth", about 11,400 km |
The distance on the Gleason map had to be scaled from the Equator to North Pole distance of 10,000 km.
For the QANTAS flight QFA27 on 10/May/2016 it was report that:
the shortest distance was 11,353 km,
the actual distance flown 11,488 km and
the flight time was 12 hrs 12 mins.
Try that on the "Ice-Wall" map.
If you don't like the Gleason's map, you can show us the route plotted on the map of your choice!