Another advantage was that it was possible for (skilled) humans to read the contents by pulling the tape through their fingers while holding it up against the light. At IBM I worked with a couple of graybeards who could do this.
At one time in my life I spent many hours every week decoding MS1553 traffic.
basically, 4 digit hex numbers.
after about 6 months i was able to subtract in hex. and add. in my head. without writing anything down.
some parameters where in 'BAMS' (look it up, it is cool). could look at 2 4 digit hex numbers and understand the magnitude of the angle differences without thinking about it.
Would ordinary tape work? Paper tape was lightly impregnated with oil to lubricate the punches and the tape handling mechanisms. I'm surprised that tape would stick to it very well.
my experience was with an ASR-33. The paper was not oiled and it did not travel all that fast through the reader.
yes, i used ordinary scotch tape.
how it was done:
punch your 'patch'. make sure there are a couple of feet of nothing before and after (no data, just paper with the sprocket holes in it).
cut into the 'master' tape at the right point.
tape in your patch.
duplicate the 'master' to make a new master. the ASR-33 had a mode where it would duplicate a tape.
i don't remember how to do this on a CDC mainframe, but at one time in my life it would only have taken 15 minutes. of which 14 minutes would be waiting for my job to run.
I did one of these as a proof of concept for storing gpg keys long term, securely and offline.
My version didn't use a motor and required a human to pull the tape through, had a set of guide holes down the middle to indicate when a bit was to be read and used LEDs as both the light sources and the photo receptors.
All in all a rather fun project which worked much better than it had any right to.
Never did find a material which had the longevity of aluminium foil with the durability of 35mm film stock.
A friend had a commercial paper tape reader (don't recall who made it) from the S-100/8080/CP-M homebrew era built exactly like that. It was the 'inexpensive' version (they had motorized versions), and was finicky but worked OK for small amounts of code. CP/M actually has a built-in papertape reader device in bios called RDR: (tho it was often repurposed for other kinds of devices).
For something as short as a gpg key, you can easily use stamped brass “tape” 0.1-3mm in thickness. You can roll it like tape if it’s thin enough or just store it as a bar if your pattern is dense enough.
(Also note that OP’s version doesn’t require a motor either and can be actuated by hand, per TFA.)
Lots of people made them back in the day (70s). Not much call for it this century, but there's plenty of retrocomputing types that would likely give it a go if prodded.
For those that never have used paper tape, it had one big advantage. You could edit it. Using tape and a pair of scissors.
Storing more than 1K or 2K in a roll becomes unwieldy to store and carry around. And do not drop it so it comes unrolled !!