Gold is a very good comparison (especially since it is inherently pretty worthless much like bitcoins) but I think the core currency quality it has is the limit of supply. One of the more amusing qualities of the fallout world to me was always the usage of bottle caps as a currency. Oh sure we have a pretty much infinite supply now but in a post-war setting it's a relatively common material (we don't use rhodium for currency because it's rare in absolute terms and also very hard to come by) that isn't going to increase in volume - that said more recent games have under cut that with the sheer commonality of nuka cola, and it also seems like a rather easy currency to forge per the volume it takes to transact an exchange.

The other points you mentioned are what's really interesting to me, the verifiable property is one that physical currency has struggled with for a long term and the ledger aspect has no equivalence in physical currency exchange[1] - it's really neat!

1. Except, of course, for my most favorite currency ever the Rai stones https://en.wikipedia.org/wiki/Rai_stones which are essentially a built-in fiat currency that no one ever actually counts or carries but instead the ownership was/is tracked entirely by oral history which is amazing.