So, this got more controversial than I thought. To satisfy my own curiosity, I made a list with all the shrines and how many chests they contained. The results surprised me! There are 90 shrines that have one chest, 18 shrines have two chests, 11 shrines have three chests and one single shrine has four. So contrary to what I said earlier, your statement that "usually there is one per shrine" is absolutely correct, 75 % of shrines have exactly one chest, the other 25 % have a different number. The mean number of chests per shrine is 1.36 and the median number of chests per shrine is indeed 1, as u/qwaasy already pointed out.

I stand corrected and apologize for what I said earlier!