Supposing that Dr. A is teaching an undergraduate-level course, what would be the pros and cons for Dr. A to allow students to address himself in an "informal" manner?
By "informal" here I mean using what is employed in a number of languages for informal conversation. For example, this would be tutoyer in French or tutear in Spanish. (Hence, the question does not apply for an English-speaking classroom, but does apply for a French or Spanish-speaking one).
EDIT (clarification, thanks j91): In Spanish, French, German and other languages, the second person singular has two versions: "Tú", "Tu" and "Du" are the informal versions in Spanish, French and German, respectively, and "Usted", "vous" and "Sie" are the formal ones in the same order. "Tutear" is the act of using systematicaly the informal version and, in theory, should be avoided when speaking to a person in a position of authority.