It's crazy how much Mercator distorts the globe. I was playing around with various map projections via WebGL shaders [1] and the size problems really stand out when the map is recentered. With modern digital maps, we should really stop using old projections that were designed to work on limited paper maps.
[1] http://sxp.me/maps/ (Select equirectangular as the projection and drag the crosshairs to recenter.)
It's not really that it's old and out of date; it makes a different set of tradeoffs to other projections, and so typically looks better over small areas but isn't appropriate for a world map since the distortion becomes extreme near the poles.
This. There are a couple of different things people use maps for, but the biggest two are finding out where things are and figuring out routes between two things. Mercator throws the needle all the way toward finding routes between two things, and it is very, very good at that, but this comes at the expense of distorting exact locations and sizes of things.
Perhaps a compromise is possible, whereby Mercator is used when plotting routes between things but some other projection is used when you're looking for isolated points. Let each projection do what it does best.
[1] http://sxp.me/maps/ (Select equirectangular as the projection and drag the crosshairs to recenter.)