During the war, the police might arrest you for criticising the king.
I can do best by quoting from The English verb, by F. R. Palmer (2nd edition):
Might is also used, though mainly in literary contexts, to refer to habitual activity:
In those days we might go for a walk in the woods.
Again, could is a possibility here.
So. yes, might has the sense of what was typically the case in the past and it can be replaced by could. As Palmer says, the usage is by and large restricted to written English. In fact, I didn't recognize it as a genuine use of might till I read it in Palmer. I would expect some other construction to show that past time was being referred to, such as might have arrested/might have gone, and that's how I would use might here in spoken English.
Palmer has a hard time categorizing this usage of might and suggests it may be either "a special dynamic use of might, unless it can in some way be interpreted in terms of existential 'sometimes'".
An exampe of existential 'sometimes' is
Lions can be dangerous
which can mean
Sometimes Lions are dangerous.
In general, the use of might to refer to past typical or habitual activity is just one way that English speakers use modals in ways that do not fit neatly into a category: might as present possibility (He might be in his office), might as a tentative form of epistemic may (Might I borrow a pen?), etc.