While an interesting difference to study, the average person is not going to care about the former case. They just don't want to keep their life savings in an asset as easy to loose as their pocket money.
If I lose $1 note. It’s gone. If I recover it, then it’s no longer lost.
Of course you may choose to encode your wallet key on paper, metal, or stone granting it properties not unlike a note. However you have now compromised the security of your wallet as well it becomes no mere $1 note, rather it is a note that represents all or a significant fraction of your net worth.
But you’re reinventing money with extra steps.
But you gain some desirable properties over traditional money.
Without crypto, you don't have frictionless and permissionless transfers of arbitrary value across international borders.
Eg, if you shard a key into three pieces and each person carries one through security, did anyone actually transport the money through?