The benefit of multiple claims is separability. In your example, claim 18 might be found invalid, but claim 19, since it requires an additional element, might still be valid. On the other hand, claim 18 might not be invalidated, in which case the patent is broader (and therefore more valuable) than if it had included only claim 19.
Interesting, so the most broad claim that gets the most press might not end up being the one that "counts", but on the other hand when someone says you have to read the whole patent to know how narrow it is that's not necessarily true either, since the most broad claim could be ruled valid.
