"A lot of nonsense has been written about a perverse predilection of the public for banknotes issued by dubious banks. The truth is that, except for small groups of businessmen who were able to distinguish between good and bad banks, banknotes were always looked upon with distrust. It was the special charters which the governments granted to privileged banks that slowly made these suspicions disappear. The often advanced argument that small banknotes come into the hands of poor and ignorant people who cannot distinguish between good and bad notes cannot be taken seriously. The poorer the recipient of a banknote is and the less familiar he is with bank affairs, the more quickly will he spend the note and the more quickly will it return, by way of retail and wholesale trade, to the issuing bank or to people conversant with banking conditions."
"If the governments had never interfered, the use of banknotes and of deposit currency would be limited to those strata of the population who know very well how to distinguish between solvent and insolvent banks."
I am finding with Mises that there is little for me to add when it comes to his writing. This is true with these passages as well. In these passages he makes a valuable point: by their very nature banknotes will only be used to any great extent by reasonably sophisticated businessmen, those qualified to make a distinction between good and bad notes. For many of the rest, they will go to redeem notes quickly, not being always sure of the quality of the institution behind the note.
Faith was increased only as the government became involved, making users of notes less concerned about the true backing. Of course, government did it for the good of the poor and less capable clients...but these were the same people who avoided keeping notes for any length of time anyway.
We see this same complacency in spades today, for example with FDIC insurance: how many people think at all about the solvency of their bank? Absent such "insurance", how long would troubled banks stay in business? How much more sophisticated would depositors be about the home for their funds?
Here again, Mises does not call for a banishment of any practice (other than by implication the practice of government interference). Instead, he sees in the free market certain built-in mechanisms to minimize the likely abuses by less-than-scrupulous businessmen.