Do we thank you for not saying “Great question!”? We do

We earlier examined two rhetorical excrescences which, in their original use, typically involved an act of bad faith on the part of the speaker.

    https://worldofdrjustice.blogspot.com/2017/01/great-question.html

Namely:

(1) The Rumsfieldian maneuver of answering one’s own question.  This purports to cater to the listener, in that it (a) breaks down a statement into two parts, allowing the hearer to absorb the idea more gradually;  (b) purports to be helpful and forthcoming, in answering questions (of which there are typically several in a row).  The move is phony, since it enables the rhetorician to answer only his own self-selected, opportunistically worded  questions.

(2) The commendation “Great question!”, with which a politician or other rhetorician  crowns a genuine (and typically banal) question, posed by a member of the general public.   Phony because, not only does it embody emotional pandering, but quite often serves as a slight-of-tongue to distract the attention of the audience from the fact that the speaker goes on to dodge the actual question, and segue to something else.

An earlier-attested and familiar -- and much-maligned -- rhetorical move, is made on public signs:

(3) “Thank you for not smoking”.   Factually phony because, being a standing statement, it is of course made in ignorance of whether you have actually refrained from smoking;  emotionally phony because a straightforward injunction “No smoking” or “Do not smoke”, or a polite variant “Please refrain from smoking”, is replaced by a formal expression of gratitude, as if from someone whose heart is perennially filled with that amiable emotion, whereas it evinces really a kind of cowardice.

What all three ploys have in common  is empty flattery of the audience by an authority not wishing to appear to be one.

The maneuver also is used currently in French.  As, an actual e-mail from a French company:

Cet e-mail est généré automatiquement.  Merci de ne pas y répondre. Il ne sera pas traité.

Formerly, and appropriately, the phrase used was Prière de …  .   Note by the way that the example above is modally incoherent:  first it acts as though you have not responded and will not do so; then it says that your reply will be ignored.