This is in fact a standard migraine thing, yes - a lot of preventives won't be prescribed unless you've been down to that level of usage for at least three months, because headache genuinely is weird in that for a significant proportion of the population (by which I mean "somewhere around 50%, depending on the study") taking more painkillers than that really does both make pain worse and render at least some preventive treatments less effective.

Pretty sure that's not a factor in my case! But them's the rules of the game I'm playing, and yeah, it is... not great.