@roger,
Your original question asked why someone to whom a banknote was issued would hang on to it instead of instantly redeeming it for specie.
If you want to know what banks got out of it, the answer is the ability to make more loans, hence more profits from interest payments by borrowers.
Banks issued loans in the form of banknotes, not specie. Because they assumed that not everyone who held their banknotes would attempt to redeem them for specie simultaneously, they could issue more loans (banknotes) than they possessed in gold or silver coins (specie) or other reserves.