Eh, would not prefer the new films to be all about the Skywalkers. I do like having Rey be this nobody who turns out to be Force Sensitive and has to defeat a villain of Skywalker blood. Like someone else before here with regards to Kylo and Rey's duel - I want her seizing of Anakin's lightsaber to be a rejection of Kylo's claim to it by birthright. Not her assuming her destiny as some long-lost Skywalker.
In a way these films can still be about the Skywalkers given Kylo, but I think it'd be cool to expand it just a bit? Would also be a way to kinda expand the Jedi Order besides Skywalkers.
But I mean if Kylo and Rey are cousins, whatever. Ain't gonna necessarily ruin it for me.
To me, that's a theme that the film's have already embraced. Regardless of Rey's lineage, she is representing the light side part of Anakin's legacy. And I respect the opinion that making this series a Skywalker family feud would seem played out. My reason why I really want nay it to still be a Skywalker family feud is so that we don't immediately think of the entire family tree as being largely cursed with one white sheep in Luke. The fight over Anakin's legacy feels more real to me if it's his blood on both sides.
This is all basically coming down to perception and what we are choosing to believe. The facts are simply Rey's story is too vague at this stage to say one way or another, but people are making conclusions based on past movies. We're dealing with circumstantial evidence. There are two characters with mystery pasts in the film, Rey and Snoke, everyone else is more or less black and white with who they are.
I said this in another thread but it doesn't make a lot of sense to hold the Skywalker reveal until Epsiode VIII. If Luke is her father then that's the perfect way to end Episode VII, thematically and emotionally that reveal would signify that the first part of her journey over. It also means you kickstart Episode VIII without having to address it further. The only reason you don't reveal it is if she's not a Skywalker.
Even the phrase "circumstantial evidence" is a bit of an overstatement; there's an implied specificity to it that often involves more cohesive names and history, circumstantial evidence to me would be to establish that Luke did have at least a lover, or have Rey remember some fragment of who left her behind. Right now, I'd argue that it's more "thematic parallels" between Rey, Anakin, and Luke; all three are the main Jedi protagonists of their trilogies, all three have used the same lightsaber, and all three are prodigies with the Force.
And it's that parallel that I think is making the Rey Skywalker theory the biggest to the mainstream audience. All my friends and family who have commented on it have said something like "She's Luke's kid, right?" The qualifier at the end shows that they know there's no substantial evidence and that even the circumstantial evidence is thin.
And that ties into my argument against your last point. To geeks, there has to be more of a twist coming; this is JJ Abrams on Star Wars, we basically expect some kind of brilliant play on a Kansas Co Shuffle in one way or another. But to most other people, there's no need for the twist. And I'd argue that there's a great
dramatic reason to both use thematic parallels with Rey to hint at a Skywalker connection without stating it outright even toward the end, as you have noted: the reveal is the Lightsaber-In-The-Snow sequence, and it's the best way to execute the moment for emotional resonance without clouding up the rest of the story, and provides a great hook to the next film.
Think about this argument this way:
1) Revealing too many hints that Rey is a Skywalker ruins the fun of her escalating Force powers towards the end of the film, and distracts from Finn's more complete (for this film specifically) character arc. If we know she's a Skywalker, or have any huge reasons to feel that's implied, than its no surprise at all that she takes on and defeats Kylo Ren. We know that they kind of wanted that idea kept secret; Boyega's still a co-lead, but they gave him more clear advertisement space because they wanted people to go "OHHHHHHH..." When she grabs the lightsaber, like people did in my theater. Twice.
2) Luke and Rey's meeting is more emotionally powerful without dialogue. As much as some of us complain about Hamill getting zero lines, it might have taken some of the magic away from the moment to have them reveal some kind of family connection through blunt dialogue; the moment was about having two skilled thespians wordlessly communicate deep feelings and internal conflict while an Oscar winning composer scores the scene beautifully. It also goes directly against one of the primary flaws of the Prequels, that of saying instead of showing.
3) It adds one more powerful tug to the next installment for viewers. This film was all about leaving the situation more destabilized and cliff hanging than any film in the franchise. Finn and Kylo are down, Han's dead, the Republic's military might is shattered, and we leave not just on a questionable training scenario, but also having just had the second possible hint at Rey's parentage with her dream island matching Luke's hideout. The fact we have a thread dedicated to discussing the possible implications of who her parents were or weren't speaks to the success of that strategem. And honestly, even if the reveal is just a quiet and quick one towards the start of the film like Kylo's parentage, it'll be worth it.