I was writing a much longer post about this, but more concisely, I had a kind of horrifying idea:

Tolkien ultimately attributes the specialness of the House of the Stewards, especially Denethor and Faramir in LOTR, to their indirect descent from Elendil. The founder of their house, Húrin of Emyn Arnen, was a cousin of King Minardil on the Anárioni side, but had no claim himself (most likely the descent was through a woman). So if the weird shit we see with Denethor and Faramir is ultimately coming from Elendil, then it’s possible that Faramir’s frequent dreadful dream-visions of the Akallabêth are not specific to him, but (like the RL dream that inspired them) inherited. Specifically, inherited from Elendil.

Basically, it’s not certain, but possible, that Elendil was so incredibly scarred by the Akallabêth that non-royal descendants thousands of years later are still haunted by the horror of that moment.