Hello Sean,
Obviously there will be other views on this but here is the one I ascribe to in my practice and teaching.
First and foremost, if the student is feeling great I tend not to tinker. While it is not the purpose of Yoga to “feel good” it is far more important to feel good than it is to fit some distorted societal image of the external body shape. I see many externally “fit” students who have internal issues (digestion, respiration, circulation et al) simply because their view of Self is myopic.
Additionally, Yoga itself is not the blue or red pill. It really cannot be prescribed as such (with effectiveness) and it is ever so slightly irresponsible of teachers to do so or allow such an idea to fester in the consciousness of students - when preventable.
More pragmatically, the human body cannot spot-reduce fat. If your belly happens to be YOUR last bastion of storage or “favorite place” then you would have to be lean all over to get at that store. Targeting is very challenging if not impossible.
Finally, certain methods of tightening the belly are externally attractive but do not serve digestive function. Again, there will be differing views here but a belly that can be softened is critically important.
I hope this helps.
Gordon