With a human face
In the Internet age, I believe Mercator remains standard because it’s easy, since image buffers and UI viewports are implemented as rectangular arrays. For example, when you click on the map the pixel coordinates can be converted to (lat, long) just by scaling, without having to do complicated coordinate transformations.
What you see in stuff like Google Maps or OpenStreetMap isn’t plain Mercator, it’s a variant called “Web Mercator”
And the US DoD doesn’t like it because it introduces even more deviations than plain Mercator.
It’s all about your intended use. If you want to use Google maps to get to work, the DoD has no problem with web Mercator on the maps backend that serves up your map tiles.
If you’re firing up Arcmap for a GIS project, using the map to navigate based on earth features, or making a reference map, of course the DoD or anyone else, wouldn’t want you to use web mercator
And no projection is perfect they all introduce weird things, like this equirectangular map which is not conformal or equal area.
This one has been mentioned a few times: https://en.wikipedia.org/wiki/Kavrayskiy_VII_projection
