Assuming that the said « open society » will not allow some members to concentrate so much of it that some others will depend upon them...

But aren't banks anf the govt already tracking down cash notes serial numbers?

I'm willing to bet that physical banknotes will be more or less phased out within a decade or so. Within the context of the fiat system, they're as free and anonymous as it gets, and that won't be tolerated for much longer. Good thing we've already got a vastly superior replacement.