I was hoping the sheets of the bordered cards would show what I was thinking a bit better.
Here's a better example. Billy Goodman, on the sheet his entire hand is there at the left, and on the right there's more belt showing. On the cards as they were sold the edge of his hand is cut off, and the edge almost always touches the edge of the belt loop at the right.
(Shown for everyone else, I'm betting you've got at least one

)
So I'm thinking they cut a strip out from between the cards, I looked at a few others and they all are both narrower and shorter than the sheet image. Most don't show it as well as Goodman.
The adapting to other machines was a guess as to why they'd do the cutting that way, which does take more cutting. The competition being gone by the late 40's is a good point, so it probably wasn't for that.
Probably for quality then.
Steve B