[traspler]

But your suggestion still involves a hard dependency on a centralised authority. Someone needs to issue the paper form, issue the stamp, make sure every agency knows what is "genuine", issue a "number" to be written on the paper, create a centralised system where that number and your ID is linked and stored so the border people can check the validity of the number, you need to procure all of these physical goods and send them to the locations. AND they have to somehow then make sure that any other country can take that paper and somehow validate that it's actually genuine as well, maybe call a phone number on the paper and ask?

I honestly don't understand how any of this is simpler, less centralised and a benefit to the end user.

If you have a web browser, a printer and know how to copy paste you can issue a pass. The system returns a pdf you can print and hand to the person. No mobile phone, data service or email involved. This can happen at the same place where you get your vaccination.

For the end user and the intermediary at the issuance place it's exactly the same, you get vaccinated, someone enters it into a form, you get a paper to take with you. With the benefit that if I wanted I could get it on my phone and someone in Spain or Sweden or wherever would be able to validate it in a second.