Say a bank’s customer has x in an account, why could they not just print as much privately as their customer has in the bank for that customer as their legal tender? Possibly as the only, most money moved around is digital, it’s pretty much on the border as theory and reality, really your not going to feel that wound.
But at least an honesty listed amount held in all accounts could be a standard in which printing it centrally could be, but it would just as well if your printed paperish cash no more or less than what you actually have in your account, who would know this better than your bank? As long as they all have their authenticators, course central printing has an advantage of avoiding issues, you know they will pass ID laws for using it on the guise of “security.” As long as that is avoided the bank printing may work.