Well, elcaps do distort with increasing voltage across their terminals (as when used in filters like those crossovers), as has been shown by Douglas Self. But certainly much less than the speaker they feed.
And what about coils with a non air core (e.g. ferrit core)? AFAIK they start to distort when the core is driven into saturation. The designer of the crossover has to make sure that this does not happen below specced power.
Although it is not that critical as one might think, IMO elcaps and non air cores should have no place in crossovers of high quality speakers. Unfortuntaely these days you can find them even in Revel F208 crossover.