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.
Always appreciated this Beck song, that has what I assume is a programmed drum beat, for having a kick drum strike near the end of the loop that seems deliberately off the beat: https://www.youtube.com/watch?v=xvGjG_cmecU