Maybe. But the fate of Middle Earth only rested upon Frodo and the ring, and they could at least have taken him (although Gandalf would probably go with him, and Sam would probably find a way to join him.)
Aragorn falling off a cliff wasn't in the book, so when I first watched the movie I was like 'Wait...what?' But when Sam and Frodo are on the rock, it's sad, because they're reminiscing about the Shire and you realize that they know they're going to die, and you just feel bad... Also, haven't you noticed that the eagles fix everything?
Probably when Frodo leaves the Shire to go across the sea and leaves Sam and Merry and Pippin... :c When I watch that part in the movie, though, I kind of laugh because I saw an interview with the actors and they were complaining about how awful the scene was to film because they basically had to cry all day. It was even worse, though, because one of the actors wore the wrong costume on one of the days of filming and they had to re-shoot everything they had filmed on that day xD