A bench jeweler has little control over store policy if they are employees. If you work for an operation that offers While You Wait repairs, that is who you work for.
Having said that, as a professional craftsperson you should have the power and the right to set limits on exactly what gets “while you wait”, and what needs to be handled differently.
As Jerry has suggested, it is not just what you can do at the bench, but your professional assesment, instincts and ability to spot and avoid problems that are the mark of a good bench jeweler.
See if the shop is responsive to the concept of a multiple tracking system, where more complicated, difficult or dangerous repairs are given a longer turn around time, as well as a price that reflects the degree of difficulty. There can be more profit to your employer with this system, if done correctly.
I too hate the current wave of lightweight, shared prong, practically not-set jewelry, that starts to shed stones like dandruff if you even touch them, but doing repairs for multiple retail jewelers they are a fact of life. Examine them closely, to spot the problems, discuss the issues before you begin work, and try to get the shop to price and time the problem work to make the shop a profit when you do have to take more time to check, to tighten, to reset, or reprong a POS.
As mentioned elsewhere above, a bench microscope, and a laser will go a long ways toward avoiding and, or solving problems with the type of jewelry being discussed here.