About the original question,
if Faramir had for some reason (picture him
hearing about PJ's Gandalf assaulting his father
) challenged Aragorn's claim the chances would have been strong for him being successful, or at least
fomenting a significant civil war. Just recall 1) the kinstrife and 2) the rejection by the Council of Gondor of Arvedui's clearly legitimate claim to the throne of Gondor. Of course, Tolkien got around this possibility by killing off Denethor and Boromir and making Faramir a "scholar-warrior" without the drive and ambition to be a king (or PM or president nowadays). And going as far back as Numenor "good" people were repeatedly prone to error, arrogance, etc. However, a big factor in Aragorn's favor, probably more then his leading the Army of the West to the gates of Mordor, would have been his role as "the Liberator of South Gondor."