I just noticed two things about the preposition per. It is usually followed by a bare singular noun phrase (i.e., one with no determiner aka specifier). This is odd because singular NPs almost always require a specifier unless the head noun is a proper noun. We say, take one pill per day, not *take one pill per a day or *per days.
But even more interesting is that sometimes it is followed by plural noun phrases, almost always specified by 100, 1,000, 100,00, etc. (e.g., The abortion rate had dropped from nearly 30 per 1,000 women of childbearing age, to less than 2.) And then when we speak this, we typically say per thousand women, instead of per one thousand women. So is thousand functioning as a specifier in thousand women?
By the way, you do find examples like a 0.75 ERA and an average of 15 strikeouts per seven innings, but these are rare.