There’s a very important element to Aragorn’s re-conceptualization that hasn’t been mentioned by others.
In the book, Aragorn is Elendil’s heir. In the movie, he is Isildur’s heir.
Now of course he is both of these things in both versions. But the book stresses Elendil as Aragorn’s heroic forefather, while the movie mentions him by name just once (as the owner of his sword), and relentlessly stresses the failure of his son Isildur.
In the book, Elendil is a figure that everyone knows and remembers and regards with utter reverence and admiration. In the movie, his fame appears to have been entirely overshadowed by Isildur’s. In the book, no one outside a handful of the Wise knows of the One Ring or of Isildur’s refusal to destroy it; in the movie, these facts appear to be widely known.
Indeed, in the movie, the Ring is famous. I believe that this change was the first and most obvious one that Jackson et al made when they sat down to write a screenplay. If Frodo is carrying this terrible token, you want everyone to react to it accordingly, immediately, with the proper awe and dread. And you do not want to waste any time explaining again what the Ring is, e.g., at the Council.
This difference in the Ring’s fame is achieved by having it taken from Sauron in very different circumstances. In the book, the massive Battle of Dagorlad where Sauron’s forces are defeated by the Last Alliance of Elves and Men takes place seven years before the defeat of Sauron himself. Barad-Dur is then besieged. Finally Sauron emerges and there is a final duel-like encounter on the slopes of Mt. Doom (Tolkien never explains why it happens there), Gil-Galad and Elendril vs. Sauron. The only surviving witnesses are Isildur, Elrond, and Cirdan the Shipwright.
Tolkien thus takes pains to establish that no Man, of any stature, witnesses Isildur take the Ring from Sauron. Even the potential extra witnesses that are Men have been rendered unavailable (one would expect two Men to match the two Elves): Isildur’s brother Anarion has already been killed in the siege and his eldest and most trusted son is presumably ruling in the absence of Elendil and Isildur. His two younger sons are absent guarding Minas Ithil, and of course Elendil is killed while rendering a killing blow to Sauron. All of this is designed to make it credible that anyone in Gondor who knew of the existence of the Ring would believe it then destroyed. The movie eliminates the seven-year siege and combines the battle with the showdown, making for a much more dramatic scene, but in doing so it means that a great many people, doubtless some of them Men of stature and rank, see Isildur take the Ring. It is thus quite credible that it is widely known that he failed to destroy it, and that he was eventually killed when it betrayed him.
In other words, in the movie Aragorn is not regarded as the heir to the greatest lord of men to walk the shores east of the Sea since the breaking of Beleriand. He’s regarded as the heir to the biggest f***-up. He has a lot to prove, to himself, to others, and on behalf of all men.
I think the change in Aragorn’s character follows necessarily if the Ring is famous and its fate widely known. I agree that Jackson and his screenwriters were almost certainly looking to give Aragorn a more obvious story arc than he has in the book (specifically, one that would encapsulate the arc that he had in the book’s deep back-story), but I don’t think that what we see on screen derives directly from that desire. I think it fell in their laps when they worked out the consequences of making the Ring famous rather than obscure.