Good questions, but they hit the limit of my knowledge of the subject. It has been suggested that by exercising and toning one reflex, if that whole indeed the way this works, you could be neglecting or weakening other aspects of the homeostatic system. But there is no evidence of that, nor anyone looking that I know of. It's just people following the same train of thought as you are.
HRVB may work best for those who have clinically low HRV to begin with, or a lot of symptoms to begin with, and work less well for those with less problems. A ceiling effect.
You could hypothesize that HRV and whatever control mechanisms are influencing it are suboptimal in most people because of stress and nutrition and most people will benefit from some hack such as this special breathing rate which throws a wrench into the works(in a good way, whatever the good idiom for that is). Whilst not necessarily indicating that people are deficient in slow breathing. But maybe they are, I don't know.
All that 6x/min breathing rate does is create a resonance on one biofeedback loop by getting blood pressure, breath, and heart rate exactly in phase, but there are other resonances with other biofeedback loops that may be equally or more clinically effective for same or other problems. The balancing of all these loops may be the reason why we don't just breathe at this rate that syncs with the inertia of the blood in the veins, which would seem to maximize the efficiency of that particular system.
For example blood vessels have their own timing for expansion and contraction. And there are cycles that have to do with the stomach and intestines and peristalsis. If you can breathe at a frequency to match those ones you could probably tone and amplify the response of a different body system by creating resonance. Breath is only one tool, but a good one for now. It's just a way to change things up. Nutrition, exercise, something else could improve the same parameters. But slow breath seems safe given its long history of use in meditation, even if it is a bit of an artifice or not the direct cause of too low HRV. Also seems safe because of the wide range of conditions this benefits. It isn't making some worse and some better.
There are some studies I think briefly mentioned in the article on Future of HRV, that muscle contractions, being shown images, and other things that take advantage of that same resonant frequency have a similar HRV effect.
Some known downsides of HRVB are you have to breathe slowly AND shallowly or you will get hyperventilation symptoms. Many people say to breathe slowly and deeply for anxiety, but that can backfire if an anxious person starts to feel numb, tingly, dizzy, etc. In professional HRVB sessions they hook you up to a capnometer.
And there is one case article on a woman getting nauseated and headaches at first after sessions perhaps due to a "parasympathetic rebound" effect. They thought that system came online a little too strong in response to previous sympathetic dominance. Those are the only contraindications I know of.