Let's use gold as an example. We all know the story of how banks started issuing paper notes that could be redeemed for gold at the bank. This way, the paper becomes a bearer asset as well.
This is the same scenario you're suggesting with Bitcoin and ecash, where Bitcoin is akin to gold and ecash akin to the paper notes.
However, what if instead of issuing paper, the banks could hammer the gold thin enough to become paper-like? Do a google search for "Gold Backs". I don't think they had the technology to create these Gold Backs way back in the day, which is why they went with paper notes.
Mint software can be written in such a way that we get the bearer-asset properties of ecash, without exposing ecash at all. Similar to how we could use Gold Backs instead of paper notes. (it's a rough metaphor, but work with me).
The code can be written so that the ecash piece is treated as a DB layer only. We don't have to acknowledge the bearer asset part of it. I mean, we acknowledge it by calling it an "internal, decentralized database". Internal to the Mint. We already have Bitcoin as a universal, global, external decentralized DB.
If new ecash is created and destroyed every time Bitcoin leaves or enters the Mint, then there is a 1-to-1 relationship between Sats and ecash. So why not just display the Sat value at all times to the users of the Mint? Why does the ecash layer need to be exposed? It's just the DB layer. But it's up to us to keep it that way and prevent people from trying to turn it into another form of shitcoin.
As far as your banknote example, I think it is apt. I agree that ecash tokens will probably function like such notes, with a market developing to help people determine the real value of tokens issued by various mints.
The Goldback analogy seems to require changes to the various ecash protocols that currently exist, and that's way beyond my paygrade, but if you have ideas about it I hope you are able to implement them.
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