To be fair you either produce a globe that faithfully reproduces the geoid (a sphere should do for most cases) or you'll always distort something on the map: an

To be fair you either produce a globe that faithfully reproduces the geoid (a sphere should do for most cases) or you'll always distort something on the map: angles, areas, distances. And then there's the question of the overall map shape: you can get away with less overall distortion at the price of partitioning the map into more pieces (as done e.g. by https://en.wikipedia.org/wiki/Dymaxion_map https://en.wikipedia.org/wiki/Dymaxion_map). The Mercator projection has the advantage, if indeed it is one, of being rectangular. To me, a shortcoming of the Equal Earth projection is that it makes places like Australia and Alaska look like they're somehow 'on the fringe'.