An office looking for a hygienist to anesthetize the doctor’s patients is probably a high-volume office. Of course this is a generalization, but if an office needs someone just to do local anesthesia, it’s because they are seeing a lot of patients and don’t have time to do it themselves.
The first office I worked at out of hygiene school was a very high-volume office patient-wise, and many times if I had a cancellation, I would anesthetize the doctor’s patients for him, so he could focus on treatment and stay on schedule (6 operatories of patients going at once).
I had an instructor for one course that worked for an oral surgeon. She was a pro at figuring out the maximum dose of each anesthetic she could give, down to the decimal point. Seemed too intense for me though!