Officers at passport control aren't trained health officials. It can be hard for them to make sense of certificates and understand what vaccinations are valid and which aren't, or which no longer are. That is why governments want to present an app where trained officials at the health ministry have already decided if the person is safe for travel or not, and just show border control officers a green check mark or no.

What is irrelevant again, because those officers will read the QR code with a computer. The computer can summarize to them how valid the vaccine still is.

There is no reason at all why a paper printed QR code can't tell exactly what vaccine you have taken, when you took it, who exactly are you, and what authority is authenticating the data. From there, any extra data is only needed at the time of reading.