Safe deposit boxes are generally governed by "best practices," not legal requirements. This is a good example.
Changing locks before box is rented again is absolutely the best practice. However, it is cost prohibitive unless you have a modern system where the locks can be changed by bank personnel with a minimal amount of training and effort. The intricate procedures for key handling and surrender are what you implement if you decide you simply cannot change locks every time a box is surrendered.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.