Those who don't care about their privacy or who want to be issuers with trustworthy reserves can use bitcoins directly, while cash customers who like their privacy can use the securely anonymous blinded cash.   That forms a two-tier system, analogous to the old privately issued money system that involved mining and storing gold (bitcoins) and issuing bank notes backed by gold (anonymous cash backed by bitcoin reserves).

The whole system could be far more secure than the old gold-reserve + banknote system, because the "gold" is more difficult to steal but far easier to securely audit, and the "bank notes" far harder to counterfeit and (especially against modern investigation techniques) more difficult to trace/identify users.   The "gold window" for these banks could be far more secure from various threats than in the old private bank note issuers.  And it's all conveniently online.