The tradition argument is about traditional storytelling rather than traditional family entanglements, I don't see them comparable at all. Hero stories are what they are.
I have some theories about Rey that might make sense of her character, but I'm not really all that bugged by her being competent at stuff. Unlike Luke, Rey had been doing hand to hand combat with her staff (as demonstrated by her use of it) whereas Luke had primarily used blasters from what we're told/shown in the first film (and we don't see Anakin getting a sabre so have no clue how he took to one). Like Anakin and Luke both she's able to hop into unfamiliar machines and use them to shoot down enemies as each did (exactly how many hours had Luke logged in an x-wing while working as a moisture farmer?). The one example you give that doesn't have a precedent in Anakin or Luke (that I can think of) is being able to hold off Kylo Ren, who hasn't exactly covered himself with glory to that point in the series, lacking the emotional control of a Jedi or the 'at all costs' focus of the Sith. She's unable to do anything against Snoke until Ren intervenes despite the fact that she had nominal training at that point, indicating that had she encountered a more competent or better trained Sith the outcome would have been different.