The intonation of the last three words may have the same root as the famous though more recent "handbag" exclamation by British actress Edith Evans. Gilbert has reported that he "decided to do a German accent" to distinguish himself from other actors playing comedy villains with Laurel & Hardy. Even if his memory of that intention was correct, he sounds decidedly more British than German in my ears. Either way, the British upper class is as much a trope in films as is the character of the German professor. Famously, the 1920 Das Cabinet des Dr. Caligari and the 1930 Der Blaue Engel had depicted authoritarian but socially inept and alienated figures that are given academic nomers. Some have taken this as far as argueing that this would be symptomatic of a subconscious need in German society for a tyrant to lead them, but the mad certified expert had taken hold in other corners of the cinematic world as well, and even earlier, cf. the 1902 French Le Voyage dans la lune, with the character of Professor Barbenfouillis "satirizing the pretensions of professors and scientific societies."
Asserting one's social position by way of titles also resonates with the British class and honours systems, of course. It ought not to be surprising, therefore, that it has been singled out for comedic effect on the Anglo-Saxon island just as much, if not more. Professor Von Schwarzenhoffen may have accumulated some six titles (of which only Doctor of Medicine and Doctor of Dental Surgery make obvious academic sense), Monty Python went all the way in the 19th sketch of their 1970 "How to recognize different parts of the body" (see here), where an omnidisciplinary surgeon has so many titles to display on his office desk that a special construction was needed to mount them all. As in The Music Box, only some of the degrees listed are potentially real. And as much as Von Schwarzenhoffen's F.F.F still possibly refers to something medical (e.g. the otolaryngological abbreviation for Fibula Free Flap), the Python sketch also pokes fun at the denominational traditions themselves: if you were FRS, FRCS, FRCP, as well as FRCOG, and trained at Oxford, it would have been perceived as less than imposing to add that you had an M.S. from Guadalajara; "B.Litt (Phil)" points not only to the confusing historical relation between the British Bachelor of Letters and Doctor of Philosophy, but goes on to joke on "Phil"; etc. (And yes, Medicine Hat is a place in Canada.)
TV and film tropes are only that because of a basis in real life. And that real life concerns not only historical figures, as for instance Horatio Herbert Kitchener, 1st Earl Kitchener, KG, KP, GCB, OM, GCSI, GCMG, GCIE, PC (1850-1916). Still today, post-nominals seem important to some. I have received emails signed "Dr. [X], BMus, MMus, PhD, Hon RCM, FRSA". And when I witnessed the setting up of a research group, with the members to be called "fellows", there was first a debate about how to distinguish post- from pre-docs (solved easily enough by adding "doctoral"), then about allowing for seniority on the post-doc level itself. For years, it wasn't clear whether a fellow was just that, or whether s/he was in fact a senior fellow who didn't play along.
In wider social circumstances, abbreviated titles can lead to "knight fever" for those who are not to the manor born: how to address someone with pre- and post-nominals, what is the right order of the titles on the seating distribution cards,...? In a professional context, it can of course be important to know who has which type of expertise, exactly. Collaborating with a PhD can be different from working with a D.M.A. (But, yes, Dr. Phil had a proper DPhil degree.)
Naturally, homo ludens sometimes nuances things into the unworkable, making for some counterefficient situations. For some, the real doctorate is only the DPhil. This is generally considered the same as PhD (philosophiae doctor = doctor philosophiae), "the most common degree at the highest academic level awarded following a course of study", but which is nevertheless only one of e.g. the 51 doctoral titles in the U.S. alone. Next to it, a number of "equivalent" doctoral degrees are recognized, for instance the D.A. (occasionally D.Arts or Art.D.), and neither the US Department of Education nor their National Science Foundation discriminate between them. Already in 1967, this Doctor of Arts degree was offered in Fine Arts as well as History, English, and ... Mathematics. It is even reported that a National Doctor of Arts Association (NDAA) was founded at the State University of Idaho. If only the current address were disclosed, so that one could properly apply to become a fellow.
Not all countries are that open. In 2011, the German Prof. Dr. iur. Dr. h.c. Peter M. Lynen defensively argued for a doctorate in the arts to be a dr. Art and dr. Mus rather than a PhD (see my post on The case of Germany). And despite being alleged as having "defined the differences between a Doctorate in the Arts compared to a scientific doctorate or Ph.D. degree", the 2016 Florence Principles on the Doctorate in the Arts (see here) acknowledge the different names that institutes give (p. 4: "DCA, DPhil, PhD, DFA") but nevertheless proceed to talk about PhDs.
If Peter Lynen lists two doctorates among his prenominals, one earned (in law) and one honorary, it goes to show that the distinction is deemed necessary. To boot: not every doctor becomes professor, and not every professor is a professor. In my home town (Ghent, Belgium), a conservatoire teacher is a "docent" (member of the faculty), but for international communications, some will translate this as "professor". Of course, that annoys the "ordinary professor" ("gewoon hoogleraar") at the university, who already has to contend with the fact that s/he is - counterintuitively - ranked higher than the "extraordinary professor" ("buitengewoon hoogleraar").
Outside of the DCA, DFA and PhDs, artistic research also has e.g. Dr. Artium and Creator Doctus. This creativity in avoiding the name PhD is rooted in the protection that universities seek against the possible erosion of their quality standards at the level of the PhD. Hence the issue of having 'degree-awarding power' or not. Not every country allows its universities to just start a doctoral program, so not every university will like to see Fine Arts institutes or conservatoires granting a PhD without having the necessary certifications themselves. That is why most non-university art institutions collaborate with a (nearby) university, accepting the latter to rule on the use of titles. In The Netherlands, a new artistic research doctoral trajectory will be tested from January 2023 onwards, catering to musicians who don't want to do a PhD, and it is already clear that a new name will have to be chosen (possibly 'PD', as in 'professional doctorate' - see my next post).
Even those who are still working towards getting a PhD (or an equivalent) can be confronted with issues of titles. Again in The Netherlands, the law allows those with a masters to automatically consider themselves as "doctoranda/doctorandus" (dra./drs.), i.e. on the way to getting a doctorate - whether actually enrolled or even planning for it or not. Because of the obvious confusion, a student in a doctoral trajectory is now called "promovenda/us".
There are reasons for keeping certain distinctions, even beyond knowing what expertise you are seeking to engage with. When I coordinated a doctoral program in artistic research, I got emails from a US student who wanted to know if ours was leading towards "a fully-fledged" PhD. If it weren't, she thought she might as well stay in the US to obtain a DMA, which she said was a "second rate degree", meaning that too many already had one, so that a PhD was more efficient in securing a job. Hence the professional doctorate having tried to NOT have to look for a name that isn't PhD. This is close to what is known - in The Netherlands, once more - the "civil effect". That term is used for specifically graded legal degrees in order for them to be valid for certain professional activities. If you did the mandatory years of law school but you did not take some particular courses, the civil effect is not indicated on the degree and you can therefore not become e.g. a notary. Such particular practices do not as a rule apply to artistic research, but it is not difficult to imagine a director of a conservatoire, in some not-too-distant future, having to fill a vacancy and choosing from a large number of applicants of which most have a masters and only some have a doctorate. That director may be hard pressed not to use degree ranking as a short cut. (This speculation is supported by OECD numbers from 2019 on labour market outcomes - see pp.252-253 here.) At any rate, when I was offered my coordinator job, it was made explicitly clear that this was mainly because of my degree - "we can no longer have someone with a masters running a doctoral curriculum". And the times are long gone when it looked cool to say, like one of my conservatoire friends in another century: "I think I should like to go to Paris and get a baccalauréat in something".