Many thanks to Helen Read, Craig Carter, Murray Eisenberg, Roland Franzius, Bob Hanlon, and other group members/gurus for their responses to my query. As always, a nice set of excellent solutions (for example Helen's), which corroborates how good a resource this group is. By now I think no more answers will come in.
Indeed, as Murray Eisenberg notes, there are situations in which the filling option simply does not make sense. Even then, there are other situations where it does. Suppose you have the following curve:
One could want to highlight the regions in which the curve goes above the x axis. Filling would come in handy there.