If one restricts the discussion to primary headache such as migraine then maybe one needs to broaden the discussion from the immediate local process of inflammatory pain, which may well be vascular in detail, to the general process of migraine
CGRP monoclonal antibodies appear to have a degree of success in controlling pain ( possibly to 50% pain levels in 50% of patients), but it isn't treating the migraine process.
Drs Lane and Davies in their book Migraine discuss the 'migraine mechanism' that underlies the process behind all primary headaches. I would extent their arguments further to see the process as affecting the whole brain as an interaction between cyclical excitatory and inhibitory processes resulting in prodromal/ictal/post-ictal/interictal phases with varying periods for each part. Just because the patient is inter-ictal doesn't mean that the brain isn't cycling through the ditterent phases, preparing for the next attack. The precipitating factors are of course various (estrogen levels, starvation, season in CH etc etc) as are the particular parts of the brain (migraines, true cluster headaches etc etc)
The treatment paradigms are equally varied. Prophylactic drugs have been the mainstay and are altering the excitatory/inhibitory balance, often with unacceptable side effects. Occipital nerve blocks, and more recently Botox, are interacting with what has assumed to be the trigemino-cervical tract, but may well include the vagus nerve through the solitary tract. More recently there has been a lot of research on Vagus Nerve stimulation (most recently auricular branch tVNS with the Nemos machine.
The area I am working in is with Daith Ear Piercing, something that went viral 3 years ago but has been ignored by the medical profession. The piercing passes through the point innervated by the auricular branch of the VN. I have done a survey of 3000 people with migraines and a daith piercing and the results indicate a strong bimodal split of responses, with those who respond - responding well and for long periods
Of course the group who fill in the survey are self-selected and thus the results are potentially biased to that absolute figures of efficacy are not necessarily accurate, but I have started a prospective longitudinal study and the results appear in line with the survey. The problem is that the results appear so good that they are dismissed as 'too good to be true'!!
I would suggest that Daith Piercing is an area that is worthy of further research...