I have not seen evidence that Web Mercator (Web-based WGS84 used in Google/Bing Maps) is based on a sphere. Various statements suggest otherwise - https://wiki.tfes.org/World_Geodetic_System_1984
From the 'Earth is not Round' article quoted: "Latitude and Longitude are useless for measuring distance and area because the unit of length, degrees, is not held constant for longitude, except along parallels -- individual perfectly east-west lines."
Well of course. Latitude and longitude are measures of location, not position. Points on a flat earth would have the same latitude and longitude as on a spherical earth.
The topic here is whether (1) the observations of flight time are a good proxy for flight distance, and (2) whether the distances inferred tell us anything about the shape of the earth.
The maps are flat because surveyors and mappers use plane surveying techniques.
"Geodetic Surveying is that branch of survey which deals with areas so extensive that it is necessary to take into consideration the true shape and dimensions of the earth".
https://www.tandfonline.com/doi/abs/10.1080/00050326.1935.10436447In plane surveying, used for small areas, the shape of the earth is not a consideration because it makes very little difference.
Wikipedia: "Plane and geodetic surveying: Based on the considerations and true shape of the earth, surveying is broadly classified into two types.Plane surveying assumes the earth is flat. Curvature and spheroidal shape of the earth is neglected. In this type of surveying all triangles formed by joining survey lines are considered as plane triangles. It is employed for small survey works where errors due to the earth's shape are too small to matter.In geodetic surveying the curvature of the earth is taken into account while calculating reduced levels, angles, bearings and distances. This type of surveying is usually employed for large survey works. Survey works up to 100 square miles (260 square kilometers ) are treated as plane and beyond that are treated as geodetic. In geodetic surveying necessary corrections are applied to reduced levels, bearings and other observations."
https://en.wikipedia.org/wiki/Surveying#Plane_and_geodetic_surveying