I tried to look up some reasons, but the only reason I could find is the deltoid muscle has been used in clinical settings due to the fact it is easy for clinicians to administer injections at this site and for patients to expose it. I imagine that maybe it is more comfortable for the patient as well, I just don't know.
I learned to NEVER question the nurse. ha ha. Muscles are a great place for injections for a number of reason from blood supply to the specific cells within and how the contents of the injection will be dispersed. The deltoid is one muscle they use most because to be honest, it's probably easiest to jab. It just sits there waiting . . . I also think the idea of an injection into my tricep? They don't want to hear us screaming. I get pinched in that area and I swear it hurts more than other parts of my arm.