In Shakespeare's historical plays, we find something of a study of the nature of authority, and in particular the name of the king. Richard II insists on the importance of the king's name, and insists, entirely correctly, that he is king. But, of course, what we see is that he has no significant authority -- his authority is unraveling even as he insists on his kingship, and all the insistence merely shows him to be weak and, at times, foolish and petty. All his talk about the King's Name is insubstantial in the face of a man with real power. And thus we get Henry IV. But Henry IV, a man who has seized the throne solely by force of will and competence, also has authority problems, albeit of a different kind. It is Henry V who shows the full authority of a king, and it is Henry V who shows that Richard's insistence on the authority of the king's name is not wrong: he invests his kingship with so much authority that his son Henry VI, a very weak king, is literally able to stop a revolt by merely mentioning that he is the son of Henry V. Shakespeare's historical plays are useful lessons in how authority works. A king's name is a title, and titles have authority -- except when they don't.
I was thinking of this recently having come across by accident an online discussion by a professor on the topic of insisting on one's title -- 'Doctor' or at least 'Professor'. And one of the things claimed was that those of us who do not insist on the title make it harder for those who, like the professor in question, do; the matter was explicitly put in terms of authority with students. There's no point in mentioning the professor's name; I have seen many professors sabotage themselves the way the professor in question is doing, so it is not particular to the person in question. But the insistence on title is indeed self-sabotage, and shows that the academics in question do not understand how authority works in a classroom, or anywhere, in fact. (Which explains a lot of how academics behave in political contexts, to be honest.)
There are things that carry an intrinsic authority -- we can summarize the sources of intrinsic authority as obvious power, obvious wisdom, and obvious goodness. All authority has to trace back to some kind of intrinsic authority. The Office of the President has authority because it is an obvious reservoir of immense power, and also more indirectly because of the general American belief in the wisdom and goodness, or at least wisdom-enough and goodness-enough, of the Constitution. Someone who can make whatever they want happen has a sort of authority from the power. A sage carries the authority of wisdom. A saint has the authority of goodness. But even in these cases the authority only arises to the extent that it is known, so it is the recognizable sign of power, or wisdom, or goodness, or at least something like these things, that conveys authority.
This is all quite abstract. But a title like 'Doctor' only has any authority at all insofar as it is taken to be a sign of expertise, hard work in achieving the difficult, and, perhaps sometimes, influence, which are, so to speak, small sips of wisdom, goodness, and power respectively. But we do not live anymore in a society in which people automatically assume that people with the title of 'Doctor' are brilliant; it still conveys to some extent that you can stick with something, and that you have spent some time trying to learn difficult things, but not much more than that; and, of course, nobody thinks that getting a PhD gives you influence. As conveying intrinsic authority, it is weak, and it is limited. And someone who keeps stubbornly insisting on its being given respect is like poor Richard II, with all the name of authority and none of the substance. It might well be the result of wisdom and goodness, or at least intelligence and difficult achievement, that itself should have some authority, but it does no good whatsoever to insist on it if people can't see that already. Something like a title is neither power, wisdom, and goodness, but it does convey authority if -- and only if -- it suggests these things in some way to people.
The other kind of authority is extrinsic, which is based on a sort of exchange, and a title always gets most of its value from this. If you are made Vice President of Sales it indicates that you probably have a sort of power, for instance, to hire and fire, or to talk to the right people, but this only gets you so far in matters of authority; Richard II's title was King and it gave him very little authority. You can get more authority by obviously showing yourself to be forceful, competent, or decent, but this, too, will only get you so far, just as Henry IV's obvious power or Henry VI's obvious goodness gave them some advantages but still left them with authority problems. Intrinsic authority is a very general authority. What gives the most authority in actual practice is using your signs of intrinsic authority to exchange for more immediate authority in the context. Or to put it in other words, while there are some things that give authority by merely having them, other things only give authority when you give them away.
The President, for instance, has immense practical power. But this is a general power; nobody thinks that the President is going to use nuclear weapons in most situations, or that the power he has directly applies to most of the situations in which he finds himself. The fact that he is commander in chief of the most powerful military in the history of the world is completely useless in moving most people most of the time, because it is not seen as directly applying to most of those situations. So how do Presidents move people? By giving power, or at least signs of power, to other people. Someone who hoards signs of power, like Richard II, looks weak. The person who knows how to give them freely, like Henry V, looks immensely authoritative. Presidents exercise military authority by giving signs of authority to others, which is why militaries are structured the way they are; they exercise political authority by giving other people signs of authority. President Obama was excellent at the latter form of authority: his authority with a lot of people arises from the fact that he did not hoard the signs of the Presidency as his own particular authority, but made a lot of people feel that if they had a chance to talk with him, he would listen, and that he was sincerely working for their interests. This, of course, is what politicians are always trying to do, but President Obama was very good at giving out specific, easy-to-recognize tokens of this, in the form of how he talked to people, how he interacted with people, and so forth. And so people freely deferred to him on a far greater scale than they would have if he had just insisted that he was the President. (Contrast that with how he handled Congress, where he did go the 'I am President' route, and then began having difficulty even moving people of his own party who had an incentive to work with him.) This was, ultimately, the difference between Richard II and Henry V: Richard II, who was king, kept insisting that he was king, and lost everyone's respect; Henry V, who was king, made himself one of the people, and because of that the people respected him entirely as king -- respecting the kingship of Hal had become a way of respecting themselves. Henry V gave people signs that they themselves mattered; and in exchange for these tokens they treated him as mattering. He gained authority by trading his own authority for new authority, and got a massive profit in doing so. Just as you cannot be obviously wealthy if you are hoarding money (which makes you look like a cheapskate), you cannot be authoritative while hoarding signs of authority (which makes you look insecure or desperate).
All of this is about authority in general. But it all applies to a title like 'Doctor' or 'Professor'. These titles carry some authority insofar as they are seen as signs of things like power over grades or expertise in a field. But this is not going to get you very far, and if you are a title-hoarder, going around insisting that students call you by your title, you will look insecure and self-doubting, and thus not authoritative. Perhaps you could get away with it if it were just blindingly obvious that you were a genius, but not very likely otherwise. If you want to look authoritative, you have to exchange your signs of intrinsic authority to get the respect that gives extrinsic authority. This, I think, is something that is sometimes difficult for academics to grasp: your degree, and the title from it, can give people a general reason to think you should get some respect, if the public at large thinks of it as indicative of something important, but it gives very little reason for anyone to think that they in particular should respect your authority in particular in whatever particular context in which they are crossing your path. That involves a kind of negotiation, which means you have to give something to get something. Too many academics think that being academics makes their opinion especially valuable, or gives their voice authority, for particular contexts. It does not -- it gives you a general ticket that you can use in earning the respect of others, as part of an exchange. Every academic knows the student who thinks that having worked really hard on a project in and of itself entitles them to an A; academics who think their titles in and of themselves make them worthy of particular acts of respect in particular contexts are making exactly the same error. It's what you are actually giving people in the context at hand that matters.
Given this, demanding that people use your title will often be the wrong move, because it looks like an insecure person trying to force people into respecting them because they can't actually earn it. It is self-sabotaging. Of course, there are exceptions. It's a great way to show contempt to people, put them in their place, or throw them off balance rhetorically by framing them as rude. One hopes you would not be doing this in a classroom, but icily insisting on one's title is one of the most effective uses of a title. And if it really matters to you, it is indeed possible, as noted above, to frame it in such a way that it is a way of giving power to students; you have to avoid looking like you are either demanding or begging. Most students prefer to use some kind of title to begin with, because it helps to establish the boundaries and guidelines for the interaction (and reduces the risk of accidentally getting too rudely familiar with the person who is grading your work). But even then, again, the only effective authority a title carries is that it can be exchanged; the students have to be getting something from the exchange. There are certainly other ways to do it than to give your title over to them (thus giving them the authority to decide how to treat your title), but they need to be getting something.