I've been thinking about the royal bloodline and I think I've come up with a suitable theory to explain how it works that fits the story.
Basically, to be considered to have Royal Blood, you need to be a direct descendant from a "True King" (a Founding Titan with royal blood, like Karl, Uri or Frieda) up to the 3rd generation of descendants. That means only sons, grandsons and great grandsons (and daughters) would have royal blood. Any great great grandsons and their descendants would already not be part of the royal bloodline.
We know all Titans, or Eldians who can become Titans are descendants from Ymir (Subjects of Ymir).
We know all 3 Ymir's daughters were also the first King Fritz daughters, so that would technically mean all SoY, all Titans are descendants from royal blood.
We also know that not every SoY counts as having "royal blood". Like Eren, most of them wouldn't be able to unlock the full power of the Founding Titan if they were to inherit it. That means that, somewhere along the bloodline, the royal descendants, the SoY are no longer considered to have "royal blood" at a certain point.
This should have nothing to do with "keeping the blood pure" or genetics. We know that the power of the Titans comes from Ymir who came in contact with the "parasite". The royal blood has nothing to do with the power itself, it's just a "rule" that Ymir set upon herself because she was unable to disobey the King's commands. It's not like the King has some genetic trait, like "Golden eyes", and only the descendants with Golden eyes can become Kings, no. The genetics of the King's bloodline are irrelevant. Like any monarchy, any son of the King is entitled to become a future King.
We know that the Reiss family had royal blood, because Uri became bound by the King's Will when he inherited the Founding Titan and became the 150th King, or something.
We know that the sons and daughters of the current King seem to always be eligible to become Kings too, so we can assume that all direct descendants from a current (or previous) King have royal blood.
We also know that Frieda wasn't Uri's daughter, she was his niece. Frieda was the granddaughter of Uri's father. Because of her we can assume that grandsons and daughters of true Kings are also eligible to become Kings, and therefore have royal blood.
We also know that, as far as Rod Reiss knew, Historia was the last descendant with royal blood, besides him. That means that the "status" of the royal bloodline does not spread too far from the descendants of a true King (a Founding Titan with Royal Blood), because, if it did, then surely Rod would be able to find some distant cousin, descendant from his great grandpa who would have royal blood. Since there doesn't seem to be any, either Uri's father didn't have any siblings, or their descendants are too distant from a true King to have royal blood.
We also know that Zeke has royal blood. Zeke can't be a descendant too distant from a true King to have royal blood. Since his family was cut off from the royal bloodline for 100 years outside the walls, he can't be a descendant from someone inside the walls, like Uri's father, so he's probably a descendant from Karl Fritz. It's possible for Zeke to be a great grandson from Karl Fritz.
Around the time Karl Fritz created the Walls and moved to Paradis, he could have left a young son outside the Walls. 50 years later, that son would father Dina Fritz, Karl's grand daughter . 20 years later, Dina would give birth to Zeke, and 30 years later is around the time the story is now. So, if Zeke has royal blood because he's a Karl's great grandson, that would mean that at least descendants up to the 3rd generation of true Kings have royal blood, and probably no more than that, otherwise it wouldn't be too hard to find at least one descendant with royal blood inside the walls.
I find this theory solid enough to fit the story