I know nobody actually has to fly the plane. But don't you think they have to THINK somebody's gonna fly the plane? I mean, I can't imagine they're all going to pull a Jack and just say "I'm just going to stay here and die on the Island, because that's what I'm supposed to do." I'm thinking at least SOME of whomever is left is going to be heading for that plane, and they surely must have some thought in mind as to who will be flying it once they get there, or they wouldn't head there in the first place. So for purposes of the story or how it might end -- no, we might not necessarily need a plane. Everybody might die and thus Alt-Timeline will be born or something. But THEY won't know that.
Or, maybe Lapidus dying is the writers' way of writing-off the plane as an exit option. Like Hurley will say "Well, guess we can't use the plane, dudes, 'cause Frank is, like, all dead and stuff."
Are there any other ways left to get off the island? (Other than the donkey-wheel room, maybe?) Where is the yacht, The Elizabeth?