For the US, everything in the design of the vaccine card system was made to prevent it from becoming another social security card fiasco. They are oversized, freely distributed, not centrally tracked, etc.

If I had to guess, it was made this way on purpose to quell fears that this vaccine effort would mutate into a bigger privacy concern and discourage people from getting the shot.

But yet here we are. People want to use it in exactly the way it wasn't designed to be used.