The Mercator projection is the only 2D map projection where:
- North is always up
- Angles are correct
If that's your criteria for correctness, then Mercator is the most correct map projection. If you want a map that shows correct right-angle grids in cities when zoomed in, for instance, you don't care about country d̶i̶c̶k̶-̶m̶e̶a̶s̶u̶r̶i̶n̶g̶ area-measuring contests.
Nowadays most people deal with maps on computers. It should be possible to have a map that stores the underlying map data in 3D and projects it on the fly to your 2D display, using different projections at different scales. Maybe use an area preserving projection when zoomed way out, an angle preserving one when zoomed way in, and some kind of mix in between.
Or maybe even let the user specify what they want preserved and use an appropriate projection.
The Mercator projection was not so much a 'lie' but an essential aid to navigation because a straight line on the map projected on to a geodesic, or the equivalent of a straight line, on the actual globe.
No, a straight line on the Mercator projection does not in general correspond to a geodesic on a sphere. In particular, the only straight lines on Mercator maps that correspond to geodesics are the lines of longitude, and the equator. The lines of latitude (exclusive of the equator), which look like straight lines on a Mercator map of the Earth, are not great circles, and therefore segments of them are not geodesics.
This map and the animated version is weird, it applies the scaling uniformly to each country, but the size error is concentrated in the extreme north and south.
It makes it look like the projection is exaggerating specific countries (like it was politically corrupted to do so intentionally) rather than exaggerating particular latitudes.
... and who didn't grow up with access to a globe that is reading this article?
Maps are a tool and you need to know the weaknesses and strengths of the tool to use it appropriately.
No map will ever be 'true' and at the same time all are.