Much can be learnt about the basis of primary headaches by focusing on cranial behaviour differences between cluster headache and migraine. Does cranial immobilization improve aberrant brain/central neuronal function in migraine?
It may possible that surrounding external stimuli like noise, light exaggerate the migraine pain. Therefore, trying to rest in a quiet, dark room away from loud noises and bright lights. In cluster headaches pain may be severe causing restlessness.
Environment and Genetics are contributing factors to Migraine. As its symptoms include nausea, vomiting, and sensitivity to light, sound, smell; the chemoreceptor trigger zone, vestibules and semicircular canals may be involved. So, maintaining equilibrium and additional engagement to have balance may provoke it. That's why perhaps when on attack, the migraine people prefer cranial immobilization.
Maybe there is a different way of framing this question. Generally, cluster headaches and migraines are considered different pathophysiological conditions, even though many migraineurs have elements of CH, and the other way around.
Rabiul Alam's comments resonate with the the vestibular/gut symptoms that one can easily understand as wanting a migraineur to lie still but not all migraineurs have major problems with nausea.
If we take a simple division between the two, a CH sufferer usually needs to stride around while a migraineur usually prefers to lie still, often but not always with photophobia. A common symptom of migraine is brain fog and perhaps this is an indication of why migraineurs prefer generally to lie still
I think most of us would agree that migraine/CH pathophysiology have many similarities as well as differences. Perhaps the issue is not so much what people ar forced to do but what they prefer to do!