The only thing I can think of that would make their current setup more robust would be having the program burned into ROM and not on tape.
I mean, probably any UNIX program written in C? Bill Joy vi can run on modern computers. What makes this software substantially different than a text editor?
Compiling pre-ANSI-C and pre-POSIX codebases might have challenges, but standardization has really gotten us lot of stability here.
I'd expect conservatively written C99/POSIX code to be usable certainly for another 20 years, there is just so much inertia there
What value would that provide (than make-work for a couple of software engineers)?
Probably the most bang-for-the-buck effort would be get their existing software running on an emulator, and get that integrated with the hole-punch machine. An even then, I think the main value there would be to have a backup in hand if they have trouble maintaining that old computer hardware.
In the lingo, business continuity and risk management. When, not if but when, the current system fails, there is high chance of it being unrecoverable. Even if it were technically recoverable, can they find someone to do that work? How long will the factory stand still while the system is being recovered or replaced? In general it is more cost-effective to replace things before they fail rather than after the fact. Doubly so in these sort of cases where using the old system (in working state!) as a reference would most likely be beneficial.
But nowadays, it would probably be an agile disaster with two or three layers of managers and sales people, maybe even on different firms, if done by best practice, between you and the customer. Forget talking to the operators.
KISS is a beauty of the past.
There is no way the simple and straightforward text based solution would be made. It is more likely it would be a bloated mess with clouds or what not.
That's a weird way of putting it, but I honestly think the "modernize" all the things crowd are probably the ones that "sound indoctrinated."
So, if your "different worldview" says reflexively redeveloping the software would provide "a lot of value," then name the value it would provide. They've got a process that's worked for them for 40+ years, what exactly is the value in re-doing software that's only a minor part of that process? Does that "value" justify the cost?
Honestly, what they've got can probably be understood more as an appliance than as an IT system, and anything developed today would almost certainly take the form of an IT system, with all the recurring cost and complexity that entails.
It's a difficult thing to quantify, but access to stable supply lines is surely worth more than zero.
If you replaced the input with USB or similar, you now also need someone with IT skills if that part goes wrong.
Maybe they should replace the computer and cassettes before they run of out them.