No it isn’t. No more than a wallet key.

If I lose $1 note. It’s gone. If I recover it, then it’s no longer lost.

A $1 note being a macro scale physical object enjoys a variety of benefits such as object permanence which provide a baseline level of recoverability. Whereas a wallet key l, being a number, enjoys no such protections.

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.

You can encode your bitcoin in wallets of predetermined size, spreading your risk.

But you’re reinventing money with extra steps.

> 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.

There's no fundamental property of the monetary system that prevents transfers of arbitrary value across international borders. There's just a large number of financial regulators, border guards, etc. who will throw you in jail if you carry a big block of gold across the border or accept a large wire transfer without filling out the necessary forms. In many countries, the laws governing those forms don't yet apply to cryptocurrencies, but I'm skeptical it will remain that way forever.

That's true, and the AML laws for crypto are already becoming more strict, especially in Europe. But in practice, it will be much easier to evade those laws than it is with fiat transfers or moving physical cash/gold.

There’s also some weird technicalities:

Eg, if you shard a key into three pieces and each person carries one through security, did anyone actually transport the money through?

For the system yes, a dropped coin eventually reenters the market and a burned bill can be reprinted again. Can't say the same about a crypto wallet. For an individual though, in both cases, a lost wallet is a lost wallet.

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 you drop your wallet in a bar, there's a chance you can recover it by returning to the bar and searching for it, by the bartender or a patron returning it to you based on the address or a number in your wallet, etc. Physical money really is not the same, even for the individual.

A burned bill can be replaced because its value is backed by an institution--the absence of such an institution is the premise of crypto.