Those specializing in precancels probably know this already, but occasionally we get questions on SCF about inverted precancels, the majority of which are usually quite common.
Anyway, I was reading an old publication
"The American Philatelist" from 1916 and found this quote a valid explanation as to why these precancels exist:
"Many collectors have asked the reason for the absence of plate numbers on the Chicago precancels, also why inverts are so common. Upon inquiry I find that the printer tears off the margins of the sheet and feeds them to the press any way they lie."Thought someone might be interested in this explanation ... it was new information for me that I never realized before.
It also helps to explain why few plate numbers are found on precancels from that generation. Of course, there are exceptions (but maybe Chicago did it differently than some of these other cities?):

...and here's one with a partial plate number showing:
