@quixote @infobeautiful Here is a better Cahill-Keyes world map, without the extremely misleading overlaid rectangular grid. Instead, just actual geographic parallels and meridians are shown. Also, Antarctica is handled better, even if partially duplicated.
But as always with non-contiguous projections, there will be small or even large islands that get split, or at least separated widely from their close neighbours. And the easternmost bit of Siberia is cut off from the rest.
I am sure that if this was a widely used projection, people would also start more or less wild theories that distortions in this map projection is a cause of some foreign policies. (From Wikipedia: https://en.wikipedia.org/wiki/Cahill%E2%80%93Keyes_projection