As a current PsyD student, reading this post was insightful, and so I want to offer another perspective.
The best supervisors I have worked with did not emphasize their titles. Instead, they recognized that respect was less about their title and more about how they related to trainees (i.e. by being a nice human being in the room) while maintaining good boundaries about the hierarchical role that everyone already knows they hold. Of note: I have had supervisors that I fondly referred to solely by their titles, but they never had to ask or emphasize those titles.
From a trainee standpoint, emphasizing the "Dr." title with interns often communicate that the supervisor likely cares more about the power differential than their supervisee. As interns and externs, we are already extremely aware of the power dynamics and hierarchy that exists in the supervisor- trainees relationship, so when a supervisor emphasizes the need for the "Dr. title" it comes across as power play on the part of the supervisor even if that was not their intent. As such, they are often perceived as impersonal, uncaring and/or unapproachable. The reality is that most interns would call you Dr. XYZ anyway and the ones who do not are probably not being "intentionally" disrespectful OR if they are being intentionally disrespectful, they would do the same exact thing when they call you by your "title."
I believe that respect is not defined by the title a supervisor holds, but by how they carry themselves in that role. You can maintain hierarchy and authority without a title because the nature of your position already secures your authority (i.e. it clarifies power differential). As a trainee who grew up in a culture where respect is highly valued, I often call supervisors by their title until they tell me otherwise, but to be honest, the boundaries and respect I have for them does not come from using their "title." If anything, the level of respect I already feel is diminished when a supervisor emphasizes their "Dr. title " because it comes across as if they have made assumptions about my character (i.e. they have assumed that maintaining hierarchy by emphasizing the Dr. title" is the only way that trainees can be taught to show respect or maintain boundary).
In situations where trainees call supervisors by their first names when not invited to do so, it may be more useful to directly express concerns about that and discuss your preference with that trainee without automatically assuming their motives and intent. This is because much like a therapist-patient relationship, the power differential in the supervisor-supervisee relationship is always present, and related to individual perspectives and/or expectations.