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It's worth noting that Equal Earth isn't an equidistant projection. The upper bound on distance distortion is an order of magnitude less than Mercator's though.

What's the task here?

Casually looking at a map to understand relatively how far away things are from each other

Unless your eye can casually assemble great circle routes it's hopeless on any projection except the radial one (and then only for routes emanating from one spot)

Nobody is looking for exactness here

Equal area projections don't preserve distance.

Yeah but it's a lot less bad than how distances look on Mercator