If in the future Bitcoin will become a widespread currency, someone will notice that being digital can be a downside, because it makes Bitcoin 100% tied to the Internet, electricity and electronic devices, unlike fiat money that can exist in many forms. Physical Bitcoin already exists, but mostly for collectible purposes. If someone will decide a physical Bitcoin for payments, they will probably get a lot of Bitcoins (lets's say 10 000), lock them in and release paper currency that will be backed by those Bitcoins. It will work just like current cash, but backed by Bitcoin instead of gold, and it won't have any problems with private key ownership that you have described in your post.
In my opinion it is not a proper way to manage it because bitcoin having a 21 decimal, do you at least imagine how many coins or bills we need to issue in order to cover all those?