Well like you say its about faith , hope without promise all of the characters are having to just trust in each other and hope without any guarantee, intact most have evidence circumstantial as it is that they are wasting their time but they have the courage to do it anyway. that is what makes them the heroes of the books.
the charge of Aragorn still plays out from his pov to be about faith in the movies , we know the truth but his character cant. it robs it of drama and makes the hole mouth of Sauron completely irrelevant where as in the book that chapter is about the most tense.
But you couldnt shoot the film in the order the book was written it just wouldn't work leaping around in time and effectively becoming 3 totally unrelated stories as the book does. Infact i doubt you would be allowed to write a book like that either today
The issue for me is that by the ring being destroyed it plays out like a win for the good guys like it all culminates in a rocky fight moment, and it just shifts the focus away from the point of you should do what is right even if you loose.
dont get me wrong i dont blame them for doing the film they did it made sense the decisions they made were good. but it doesn't change the base issue of the ending is quite dramatically different and its a reasonable complaint