Is there some reason why surgeons don't want to do a corset platysmaplasty? Is it a really dangerous/risky procedure?

Facelift and necklift are two separate procedures than can be performed simultaneously. The platysmaplasty is a very safe procedure and is usually performed in conjunction with a necklift. An isolated platysmaplasty can sometimes be performed without a necklift, but there is a risk of creating too much loose skin and then you would need a necklift. This is perhaps the reason your surgeon elected to not perform the platysmaplasty. Again, the procedure is extremely safe and the risk is that following the platysmaplasty you may need a necklift to remove loose skin. 

Thank you for your question.   For the pictures you send you need a platysmoplasty to treat the platysma bands.  The corset technique is only  one other of the techniques use to treat this condition.  That technique doesn’t offer a major risk that others in the treatment of the neck bands is only a preference of the surgeon

Thank you for your question!  I am sorry you are having these issues after your facelift (and I am glad that you are pleased with some parts of it).  A platysmaplasty is a very safe procedure, and it is typically performed during a face and necklift.  A small incision is placed in the natural crease under the chin, and the muscle that causes the 'banding' in the midline of the neck is tightened to improve this area. Not all patients need this procedure, and it is important that you have an evaluation with a board certified facial plastic or plastic surgeon who performs these regularly.  I would need to see you in person, however you may be a candidate to have a platysmaplasty under local anesthesia.  However, I would also recommend giving your results some time so that you are fully healed before undergoing any more procedures (at least 6 months).I hope that this helps!-David Gilpin

That is not procedure that can be performed on every neck lift patient. Underlying anatomy of platysma muscle and neck deformity will dictate the form of platysmoplasty patient needs. Considering how close your platysma bands are now, it is very likely that you could have that done with your previous surgery. However, if your surgeon was not comfortable with it or did not considered it necessary, you have to take it as a part of his decision and element of safety. Distal platysma plication can be completed through existing submental incision in local or twilight anesthesia, again depending of surgeon experience and comfort. Good luck.

Doing these answers I have noticed that many people have the same complaint as you. Apparently there are a growing number of plastic surgeons or dermatologists or  facial plastic surgeons, mainly young,  who were never trained in neck surgery and only do pulling from the side. This is incredibly limiting. You can't fix bands by pulling from the side.  You need to talk to  your doc. 
having said that,  your neck is not a disaster.  Corset platysmaplasty refers to a particular way of doing the neck which some docs found useful and some not.