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I think a good analogy would be to think of an excel spreadsheet in the sky to which accounts are simply cells in that spreadsheet and banks control access to those cells as well as the overall supply of cash in that spreadsheet (printing more at will as they choose).
A blockchain backed crypto currency would be that same spreadsheet in the sky where any user has access to cells in that spreadsheet by creating a "wallet" and controlling the spending of cash from those cells by using a private key to unlock that cell. The supply of cash is predetermined based on consensus protocol backing that spreadsheet and is agreed upon by its users. They partake and secure the spreadsheet because of the rules or "formulas" controlling it.
i.e We trust banks with our money. Blockchain is trustless in its native design.
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