This is an interesting idea, but I already think Luke has a more compelling reason for being in exile. This concept, which would be hard to explain beyond the opening crawl, makes things overly complicated, in my opinion. I also think most people would scratch their heads at the idea of Luke being the heir to the Empire, since that isn’t really established as being an important thing, the “throne”, I mean.

Personally, I think the reason Luke is in exile in the films works, and doesn’t need to be explained in the opening crawl. Han tells them why he left in the Falcon scene, and not knowing the details from the start helps keep it mysterious.
And I know I keep saying this, but really the simplest way, in my opinion, to explain Leia and the Resistance thing is just to say that First Order spies or sympathizers have infiltrated the New Republic. Because of that, Leia had to form her own militia separate from the Republic, since the sympathizers made the FO not seem like a threat, and to keep spies from knowing what she was trying to do. I mean, it makes since and it is canon, so I think briefly explaining that in the crawl is the least complicated thing to do.