Gold is only private in small coinage. Actual wealth in gold needs a custodian. Practically, gold is not being lugged around, it gets deposited in a bank, which IDs you.

Cash is not money, it is a coupon. As a coupon it doesn't really have any constraints on privacy as long as it is a valid claim to Gold.

As I said before I am an economics nerd not a coder. I am not sure what kind of privacy is achieved with those proposed filters as I can't extrapolate what is gained from the golomb-rice set compression.