Why is everyone so afraid of partial removal of problematic submandibular glands in fixing cobra neck deformity?

First off, the purpose of submandibular gland removal is not to fix a cobra deformity. If you don’t like the “flat appearance” of your neck, taking out the gland might make it worse. I don’t recall your previous photos.
Second, I wouldn’t say doctors are “afraid” of partial gland removal. It’s just a matter of risk benefit ratio and familiarity with the procedure. The safest way to take out a gland is by making a direct incision but it leaves a scar. The posterior facial artery is best identified with a wide exposure. However, to avoid a scar with a facelift, exposure is limited by going through the preauricular or the submental incision. To access the gland, the submental incision has to be slightly longer to avoid working in a hole. True access to the gland means going under the platysma or through it. Incising the platysma eithout good exposure increases the risk of marginal mandibular nerve injury and without good exposure increased risk of bleeding from the facial artery and posterior facial vein and thus a risk of post op hematoma. A post op arterial bleed in a neck with full skin elevation from a facelift can result in a bull neck which can be potentially serious. I don’t think dry mouth is a real complication. I’m well versed in total submandibular gland removal and never really see dry mouth.  There are six major submandibular glands to the area. To those who shave submandibular prominence shows on top of the platysma might just be shaving fat and weakening platysma muscle. Usually partial gland removal requires the proper risk benefit ratio to make it worthwhile, but it is a difficult approach and is not innocuous.

Cobra neck deformity usually is the result of over zealous resection of fat from the submental region in combination with platysma muscles not reapproximated during a necklift.  Removing the submandibular glands will not remedy these issues.  In terms of partial submandibular gland resection dry mouth is probably the least of the problems that can occur if not performed flawlessly.  Facial nerve injury is by far the number one potential complication and it can occur when the gland is removed with full surgical exposure.  

 Thank you for your question.    There are possible complications but the most important part is that the surgeon is familiar   with the surgery and you indeed need the surgery.