Agree with Coke and Comics on the Rogue Cut and how it effects movie, and would also like to add that it also, well, adds more to the character developments throughout the movie, ironically except when it comes to Rogue herself who just gets in the way of the narrative and pushes out another character (who wasn't necessarily doing much anyway but is reduced to pained looking reaction shots for the rest of the movie).

Someone mentioned that there is an extended cut of the first x-men movie - if it's the one that I am thinking of, it is more that you can watch it with deleted and alternate scenes placed back but they are incomplete/not officially reworked back in and there is at least one key scene that isn't included that is mentioned, but I do think it make for an interesting look at the original movie - I think the scenes do help make for a more complete movie and a real, official extended version would be interesting to see.

The power obviously belonged to Rachel in the comics. But they didn't want to introduce a new character, which makes sense from a dramatic perspective.

It fits in with the idea of "secondary mutation" from the comics and allows that a lot could have happened in the 10-15 years between Last Stand and Days of Future Past

I think they could have gotten away with introducing Rachel though, as a mysterious possible child of Jean - they did have other freshly introduced characters like Bishop and Blink, after all. Though I agree that they probably wanted to have the character in that role to have more of a connection to the audience.

Yes, agreed - that's always part of what bothers me about the Rogue Cut and the way Rogue comes in to replace someone - I don't know if I should say anything more at the moment in case of spoilers though

But... her role doesn't make any sense! They could have found something else for Kitty to do - phase people through walls etc to escape Sentinels or something - if they really needed her in there at all (which frankly, they didn't), and could have easily introduced Rachel (without all the Jean Grey link) or some other character to do this - it's set in the future, so no reason they can't pull in any other one like they did with Sunspot, Blink and Bishop.

There's no reason they couldn't "introduce a new character for an important plotpoint" - that's what they've done in all the other movies - all the X-Men in #1, Nightcrawler, Colossus, Iceman in #2, Jean as Phoenix, Beast and Angel in #3, all the First Class crew in that film, the ones I've mentioned in DoFP plus Quicksilver; and Psylocke, yet another Angel in Apocalypse.

Yeah, giving Kitty Rachel's powers bugged me about the movie, too, but I don't recall if they ever specified what her exclusive powers were in the previous movies, so not a huge deal. I also wanted more scenery of the future X-Men fighting sentinels as that was the far more compelling draw for me. The First Class crew is fine, but I like the adult fully-realized X-Men being the X-Men and kicking butt instead of the perpetual origin story. Though Quicksilver's scenes alone are worth the price of admission for the movies he's in.

What doesn't make sense? Well, there's the secondary mutation thing, which isn't mentioned anywhere in any of the films as a possibility, but is a (stupid) feature only of the comics*; that the power pulled out of thin air is not even remotely related to her existing power-set, and is only given to her because they wanted the actress and character in the film and wanted the power for the plot, but didn't have any sane in-story reason for her to have that power or anything else for her to actually do

(* the only vague equivalent was Beast doctoring himself in First Class and turning into a ridiculous looking blue teddy bear thing, which has to have been one of the worst ever make-up / character designs of the 21st century)