GUYS. I figured it out. I don't know if anyone else has proposed this, and if they have then I'm going to feel dumb.
Cadance is to the Crystal Empire as Anastasia is to the Romanov Empire in the Fox Animation film of the same name. With a bit of Sleeping Beauty thrown in.
Cadance was born in the Crystal Empire as
a crystal pony to the king and queen at the time, so she really is the born heir to its throne. She was born very shortly before Sombra's takeover, however, and when the unicorn king attacked and enslaved the Empire, the king and queen were killed in the process. Celestia and Luna managed to defeat Sombra, learning moments after that one member of the royal family still remained - a baby, the little princess Cadance. Seeing as she had no one to care for her anymore and the fear remained that Sombra might not be locked away forever, Celestia - always a believer in destiny, of course - adopted the filly into the palace in order to properly protect her and teach her for the time that may come when she will have to return and fight for her rightful home. It was during this time and training that she realized the importance of her destiny and earned her crystal heart cutie mark. Living away from her kingdom and the Crystal Heart for so long as she grew slowly caused her to lose the ever-present "crystallization" of her coat as well. In The Crystal Empire Pt. II, though, even when she has been drained of all energy, the sight of the real Crystal Heart sparked something in her, like this was the moment she had been born for and these were her people that depended on her. This gave her one more boost of strength, and she managed to charge in and save the fateful item and return it to its rightful place. Between the return of the Crystal Heart and the realization that the rightful heir to the empire had returned, (ergo: "Behold! The Crystal Princess!") the crystal ponies could rightfully defeat Sombra for good. It would then appear that Cadance returned to rule the Crystal Empire with Shining Armor. I imagine that, if she stays there long enough, she will eventually gain her natural-born crystal coat.
And I know some of you are probably thinking: "Hoooold on a second, if she was born in the Crystal Empire when it was thriving, how could she have been a teenager when she was foalsitting Twilight?" Easy enough - one of two things are possible here.
1.) One, Crystal Ponies actually have a lifespan ratio of like, 800 to 1 compared to your typical 3 pony races. And once Cadance was removed from the Crystal Empire and the Crystal Heart (think of the Heart like the crystal from Atlantis - it actually gives them longevity), she slowly, slowly started to sway to an ordinary pony's growth span. From the time she was rescued from the empire to the time she started foalsitting Twilight, she still maintained some Crystal Pony longevity that caused her to age slower. But by the time we met her in Canterlot Wedding, it had pretty much leveled to normal aging. This would explain why some of the crystal ponies seemed to recognize Cadance as the long lost princess.
2.) Two, which I don't think is quite as interesting, is that crystal ponies have lifespans as long as anypony else - they were just in a "frozen" statis when the curse was put on the Empire. BUT the royal family of the empire, like Celestia and Luna, are the ones with 800 to 1 lifespans if not simply immortal.
Sooooo......yeah. Let that sit for a bit.
I'm now imagining Sombra singing "In the Dark of the Night" about Cadance.I was once the most powerful stallion in the Empire!
When the royals betrayed me, they made a mistake!
My curse made each of them pay,
But one little girl got away!
Little Cadance beware, King Sombra's awake!!
As the pieces fall into place,
I'll see her crawl into place!!
Mi Amore Cadenza, your Grace,