Equal-Earth is just as flawed as Mercator, just in different ways. Mercator made sense in an era of navigation based on compass measurements, astrological observations, accurate time keeping, and dead reckoning. Mercator still makes sense as a projection associated with local navigation, even in an age of GPS, for the way it preserves angles. Equal-Earth makes sense for the symbol of a global organization, but is mostly useless for navigation. Equal-Earth is really only good for global economics and politics. Waterman butterfly is my favorite for obvious reasons. Then there are the satirical map projections.

What do you mean with “best“? The angles, and therefore the shapes, are all wonky. Check out Japan on the equal earth projection and compare it to a map of only Japan.

Since the earth is sort of round, all projections will distort. The question is what will be distorted. The equal earth projection distorts country shapes more than the transverse Mercator does.