This thread is a horrid mishmash of plot, characters, tropes, cliches, and settings.
Post-Apocalyptic games, that's a
setting. Fallout 3's 'plot' was about a son or daughter trying to find their father while simultaneously trying to make their way in the world, eventually either culminating is saving or damning the world. S.T.A.L.K.E.Rs plot was about an amnesiac soldier searching for another missing soldier named Strelok (not giving spoilers), and his attempts to survive and explore the phenomenon related to the second Chernobyl disaster and eventually making a important decision.
Specifically, the plot is the 'path' the protagonist takes, like this:
Learn the difference!!
Specific elements or tropes, such as amnesia are again, are
not the plot, but can be used as elements of such from which to expand the plot. Many times, yes, it's used poorly and is a shoddy way to explain why a character is a blank slate, and so they don't have to be given much backstory. I'd guess, this is mainly to provide the player a sense that this is a 'role' they're playing of themselves. But, amnesia can be used to great effect as well, take Planescape Torment for example, about a nameless amnesiac immortal searching for the truth about his own past and seeking a way to finally die. A lesser game would have simply dropped the player in and left them to make their own way with a random assortment of quests, Torment provides an extensive history and background for The Nameless one, and yet still offers players the freedom to determine the outcome of his story.