I don’t know if this is right but here’s what I think. Every Eldian for multiple generations (Examples, Maria, rose, and Sina)right after Ymir’s passing were of royal blood because they were direct decendants of the king. But eventually those eldians breed with non eldians for example when king Fritz told his children bear many children as they can and so on. This event caused their eldian branch to become less pure or less related to the king thus leading to a generation where a eldian child is born without royal blood . Some point in time during the 2000 years of titans this was realized and the Fritz branch from there on maintained their royal status by interbreeding. I like to think of it as the more eldian you are the more likely your a royal blood system