Not sure why they didn't use squares.
A lot of the reasons seem reminiscent of why hexagons are awesome in video games: https://www.redblobgames.com/grids/hexagons/
I know that they are associated with rpg board games and therefore have found their way in to 2D RPG video games as well. I can see a slight advantage to using them on a board game situation where it would make it more accurate to estimate diagonal distances by counting tiles, but in a computational situation where your box can compute the Pythagorean theorem a few million times a second, the benefit of using hex systems in games eludes me.
I'm very curious about H3's lat/long => hex cell system. I'll be studying their geoToH3 function soonest. https://uber.github.io/h3/#/documentation/api-reference/inde...