It's not principle. It's lore/mechanic disconnect. If the lore was that a medusa turns you to stone with a gaze, but the written mechanic was that you turn to jell-o, there would be a problem. Lore and mechanics must match.
And yes you are correct that feats would not be enough for aasimar, tiefling or any other race achieved via a feat. You would remain whatever race was chosen before the feat and simply have a few more abilities. You might as well take human, pick the magic initiate feat, and then claim you are the Santa Claus race. Feats don't change what race you are.