It is true that anonymous coins would prevent data-mining of one's spending habits. Real anonymity, by contrast, would mean account- holder anonymity. Such a system would also provide a mechanism for transfers between anonymous accounts, which could take place for whatever reason. Possible business deals between account holders are not the business of the bank, and there is no reason for the bank to collect any information on the identity of its customers, or to know anything about such business dealings. Rather, all the bank would need to do would be to make anonymous, authorized, secure transfers between accounts.
Money serves two principal functions.
It is a medium of exchange, and it is a store of value. A few digital cash systems seek to partially anonymize money in its role as a medium of exchange. But anonymous banking accounts would also anonymize money in its store of value function. There is nothing wrong with, or unattractive about, anonymous digital coins and anonymous small- denomination payments, of course. But a true system of anonymity would allow anonymous digital coins to be withdrawn from anonymous banking accounts, as well as to be deposited into anonymous banking accounts.