Good point. How you "write" a piece of music, or how you "count" it, is simply an aid to performing it.
Another kind of example: the intro to Led Zeppelin's
Rock and Roll is best written/counted as starting on "the and of three" (that is: one ee and a two ee and a three e AND). You play the first note on the AND of three. You COULD count that note as 1 (there is no "law" against that). But if you did, the count wouldn't make sense for any of the measures in the rest of the song.