A few issues
It was suggested in The Tale of Years that a reason why Arvedui's claim was rejected was because he was the last of a line of losers, who allowed Arnor to be fragmented into three, with only one part surviving, and now under threat from the Witch-king. Why should he be made King of Gondor, with the resulting risk of diverting resources from there to prop up a 'failing state'?
Later, Arthedain was destroyed by the Witch-king, although at the price of the latter's defeat. Arvedui's son and later descendants took the title of 'Chieftain', laying aside their royal status, there being no kingdom left to be king of.
This made later Gondorians, including the Stewards, uninterested in trying to find out if any descendants of Isildur, through Arevdui, still existed, let alone making an offer of the crown of Gondor. The earlier prejudice would be magnified, in terms of not wanting any scarce Gondorian resources being diverted to resurrect a 'failed state'.
This shows the huge obstacles Aragorn II had to climb to be considered a serious candidate for King of Gondor. What I feel was crucial was his ability to defeat Gondor's enemies, as Eärnil did centuries before.
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