One could imagine that a certain set of adjectives or nouns instead of being expressed with the regular copula, instead were expressed with an habitual form of 'to become', and this would reflect some semantic property of these nouns or adjectives – maybe they are only expressed fleetingly, or they are less intrinsic properties, or less obviously intrinsic properties. Properties which only are evident on occasion.
One could also of course have some kind of systematic distinction marked this way as well, but then again, what's the actual difference between two similar verbs like 'be' and 'become (regularly)' if not a systematic distinction? What I want to go for here is maybe something that is more un-subtle: a difference greater than that implied by the actual "usual" semantic difference - with some nouns or adjectives, maybe 'become (regularly)' marks some kind of disdain or some kind of respect or whatever? Fear? Hope? Whereas the use of a copula would just be neutral, or even +(mainly neutral) +(precluding the particular thing implied by the habitual for this set of lexemes).