The system has 2 off host and 1 off service connections is accepted by most readers or hearers because they think it’s some kind of jargon they can basically understand, even if they can’t cope with the full details. You are right; they are wrong but it’s not a mutation of of as in I’ll need 3 of these cables. It is, as you think, simply incorrect and yucky. It does come from request sheets, but only by mistake
3 of and 3 off are different uses from different roots through different routes.
3 of is ordinary English and might refer to packets of cornflakes, bicycles or anything you care to mention. It does matter slightly that three of those doohickies will generally come from stock, not any kind of special order.
3 off is not ordinary English even though many people mistake it for 3 of or think they’re interchangeable. 3 off is correctly used only in fields like manufacturing, printing, baking or bottling and other production situations… never retailing.
I’ve seen every stage of this in building aircraft and their components, making safety helmets and printing periodicals. Different items; different methods; identical language.
Whether in a traditional forge or a small workshop or a new-fangled assembly line, the workspace generally has to be re-organized for each item and a decision taken as to how many examples to… uh… run off. This is true whether I’m turning them out for stock or to meet a wholesale order from a specific customer… which requires such usages as This is a custom run… 200 off.
I might run off one or a dozen proof copies of a newspaper or a light-fitting, then run off as many more as are wanted this time. Thus the in-house trial might need the line to run 3 off and the next day’s production might call for 300 off, meaning nothing more arcane than run 300 off the line.
Anywhere production and retail people or premises overlap both customers and less-specialised staff hear but don’t fully grasp the workshop instructions and mistakenly switch the terms.
Strictly, filling the boxes with cornflakes doesn’t come into this but the box factory might run off 30,000 items per shift while at the other end, the family buys three of those filled boxes.