As the “exception that proves the rule”, there’s a fair bit of dance music that intentionally goes off grid to either build tension or sound more organic. There are even entire subgenres dedicated to sampling more acoustic and traditional instruments (usually percussion) while embracing underengineered sound.

Yeah, especially for a high school band. I'm sure budget was limited and they probably didn't have time for retakes. Playing to a click isn't easy, and playing to backing tracks not perfectly in time with a click is even harder. These are high school kids and professionals will tell you this isn't easy. Given that they probably didn't have time to go through and manually clean things up, you snap it to a grid so it doesn't sound like a mess.