They easily had 6 movies post ROTJ before killing off the skywalkers.
First trilogy: set 10-20 years after ROTJ. The end of the battle with the remnants of the empire. Palps comes back.
Second trilogy: set 15-25 years after ROTJ. Focus on the skywalker descendants and how their line ends.
I think this is exactly how they planned it though. The Sequel Trilogy was going to be each member of the Big 3 get their own movie:
Awakens = Han (Leia and Luke still in the film)
Jedi = Luke (Leia still in the film)
Rise = Leia
Carrie died in real life so that threw Liea's plans off. People also weren't 100% happy with Luke story just ending like that so they switched it:
Rise = Luke, Lando, Leia (Previous Footage)
They can't "Move on" From the Skywalkers because that's the mythology of the Franchise. There will always be a Skywalker in some form in the Star Wars Story Episodes. You can do spins offs and TV shows with other stories. But the "Episodes" will probably be Skywalker centric. .George original Notes had 12 Episodes. That means the Original Big 3 were going to go out in this Trilogy with the new generation of the the Skywalkers taking over for Episodes X, XI and XII. Even Hamill said in 1983 while promoting "Return of the Jedi" that Lucas told him about the future stories.
. Rey isn't a Skywalker and it's more likely about Kylo turning into a good guy at the end of the movie, rising out of the dark into the light. Rey being a Skywalker is lazy writing because it's what everyone already guessed a long ass time ago. Reminds me when they edited Rey talking to Kylo about helping her just so they could everyone talking about "Rey is joining the dark side confirmed!"
