...Couldn't someone just look up the public address to see when the coin was first loaded?

I'm not sure why a separate proof-of-age would be needed.

And relying on a downloaded zip file to conduct the proof in the future sounds risky. Why not just have the hash be of some text printed on the card, naming the type of coin and its address? Then the card could be locked in a safe, and in 10 years when USB drives and all optical media is extinct people can still type it in to do the check