Yeah, honestly, I think you’re overanalyzing the lightsaber thing a little. Rey stole it?
Luke rejected it. Luke didn’t want it, and he obviously didn’t care that Rey had it or he would have said something. Rey even offered it back to Luke again before she left.
Honestly, I think the whole movie Rey doesn’t even think it is hers. She doesn’t think she is the hero, she is merely the custodian of this Excalibur until she finds the real hero. At first she thinks it is Luke, he rejects it twice (for a multitude of reasons). Rey even thinks Ben might be the hero later in the film, and I think she brings the lightsaber with her in hopes that he will be the one to take up the mantle. She even tosses the lightsaber to him during the battle. It isn’t until she realizes that Ben hasn’t turned back to the light does she start to accept that maybe she might need to be the hero. And clearly when Luke says he won’t be the last Jedi, referring to Rey, I think that is him being cool with Rey having the lightsaber anyway.
And sure, if you go by bloodline, Ben might have some claim to it, but I think the movie has demonstrated that bloodline isn’t the end all be all. Rey catches the lightsaber at the end of TFA because she is “pure of heart” with “noble intent”, which is what the Force really cares about. Ben doesn’t have that.
This is my own personal opinion, but I think the only reason Rey is on this journey is because she demonstrated that she is empathetic person that wants to help others, which she shows us early on in the film when she helps BB-8. I think that made her worthy in the Force’s eyes.
I’m only analysing it myself to provide insight into my comment that she unwittingly stole it. When I use the word “stole”, it is for efficient simplification of the idea that she doesn’t have it by consent. I’m not saying for a second that she consciously stole it from Luke, she probably doesn’t have a high regard for possessions and sentimental value due to her own background and so probably doesn’t feel or sense any wrong doing by taking it without actually checking with Luke first. It doesn’t change the fact though that he never gave her leave to take it, which equates to it being “stolen” or borrowed permanently without consent if you will.
Your 2nd and last paragraph is an interesting take on the matter, though I’m not one who subscribes to the force being sentient or self-aware to any extent and the whole “light rises to meet the growing dark” is a misinterpretation of the bringing the force into balance theme and a “quick fix” on Rian’s part to explain Rey’s insanely quick command of the force and try to satiate the fan criticism around it.
In regards to bloodlines, I’m simply using these in regards to Ben as a technical comparison on someone who does have a birthright to these things and not that it’s the be all, end all. Also I took Rey’s force pulling and catching the lightsaber in TFA as taking Kylo by surprise, especially with it already traveling in that direction it would only take a quick last second use of the force to alter it’s course to miss Kylo and go to Rey instead. It has nothing to do with the Force choosing Rey over Kylo as to who should have the saber, in my eyes THAT is plain silly and twists my concept of the force into something unrecognisable from what I grew up with from the OT.