Because it doesn't. HEX may simplify moving 60 degrees diagonally but makes it impossible to move horizontally and 45 degrees diagonally which are way more common. For overland maps, it's more natural for people to think about going N-W-S-E-NW-NE-SW-SE i.e. 8-directions and not 6-directions. Plus it doesn't fit with indoor locales which in the vast majority of cases have straight walls and 90 degrees angles that would cause half hexes all over the map.
Squares may simplify moving 45 degrees, but make it impossible to move 32 degrees. The argument is fairly weak. By moving sometimes straight and sometimes diagonally with hexes, one moves closer to reality than by doing the same with squares when moving in any direction (unless one uses the 1.5 square rule of 3E for a diagonal).
In real life, people tend to move the shortest distance and rarely move only 0 degrees forward/back, or 90 degrees to the side.
Btw, offset squares have the same advantages as hexes, but allow for rectangular rooms easier.
Squares have all of the problems of hexes and more. Hexes have fewer problems than squares (course, some of those problems like diagonal flanking disappeared in 5E because flanking no longer exists).
Finally, drawing a square map yourself is a piece of cake, drawing a hex map is a cake of pain. This is why the game just naturally evolved towards square maps.
Totally non-sequitor. There are many FRPGs that use hexes, just like there are many that use squares.
Hexes have their own benefits (better circle area spells, better 60 degrees wide cones - but worse square areas and 45/90 degrees wide cones), and many fans, but sorry they are a minority.
Cones in 5E are a little over 53 degrees. Closer to 60 degrees than 45 or 90 degrees (although they are only a little bit closer to 60 than 45).
And even squares are poor for designing rectangular shaped rooms if the room is not "x times 5 feet" by "y times 5 feet" in dimensions. People are so used to the perfectly aligned rectangular rooms (15 x 20, or 25 x 35) that they do not even think that a 13 x 17 rectangular room should actually exist in the game.
By using hexes and having good half hex rules, any shape or sized room/chamber/cavern can exist and movement in it is more natural.
Despite of what I've just said, I'm not even a fan of square grids, and I'm trying to play 5e without a grid altogether.
Good luck.
