The relatively old McCann's catalogue of Canadian Booklets lists all the various staple sizes for these booklets. However, it does not really go into details about how and why as per your listed questions.
So that idea of wire fed machines sound possible. I still wonder why they had three different sizes unless the machines were adjustable and the small size staples were used to save the metal when they were running short.
I have not seen any info that suggests this though.