I don't have any advice, regarding having students "sing" in lessons (guess this would have to be a case by case or individual by individual take), but I would like to put in my 2 cents for this very valuable teaching tool.
A few years ago, after performing professionally for many years, I found myself in a bit of a "rut," breathing-wise. I was giving a solo recital in a few months and programmed one of the Vivaldi Sonatas (edited by Luigi Dallapiccola), which had NO places basically to "breathe." I decided to go to my partner's singing teacher, who has quite a reputation in NYC for "reviving" and really helping singers who'd developed problems over the years (had many students singing at the Met and NYC Operas, etc.) Maria Caruso (no relation!) Farnworth turned my playing around! I went to lessons for a few months - mainly working on POSTURE and vocalizing. Nothing too dramatic, just breathing/vocalizing exercises with piano, always maintaining a no-slump chair posture, centering one's self.
If one can breathe properly by singing properly, this translates to the bassoon or oboe! These lessons were taken in conjunction with breathing lessons with Carmine Caruso, also here in NYC. Carmine emphaized "keep the BLOW going!" But, I must say, the singing exercises helped clarify all this, by far. Of course, these steps were taken many years after I'd studied bassoon in conservatory, and only when I found I'd developed bad habits (posture, etc.). Don't know if I would have been amenable to vocalizing, as a young student! At any rate, good luck with incorporating this into lessons. Alles Gute - Jim
James Jeter, D.M.A., NYC Bassoonist
"To love human beings is still the only thing worth living for; without that love, you really do not live." Soren Kierkegaard
"Whatever you do will be insignificant, but it is very important that you do it." Mahatma Gandhi "Mach' es kurz! Am Juengsten Tag ist's nur ein Furz!" Goethe