How come not all subjects of Ymir have royal (Fritz) blood?


All of today's Eldians have a common ancestor, Ymir. But in all Eldians there
is also a royal bloodline, Fritz/Reiss. This royal bloodline came from King
Fritz. As far as we know, King Fritz and Ymir have three daughters. Thus,
should not all Eldians be also descendent of King Fritz? This only makes sense
if Ymir had kids with someone else, other than King Fritz, but that is not
shown. What am I missing? Or is it a plot-hole?

To rephrase it.  
We know Ymir only obeys commands of the royal family and that's why the
Founding Titan can only be used by those of the royal family. But, if all
Eldians are her descendants, and she only had children with the royal King
Fritz, all Eldians should be Fritz. But, that is not the case. Why?




All Subjects of Ymir are Eldians, but not all Eldians are Subjects of Ymir or
Royal.

Technically, every subject of Ymir has Royal blood, but it is not enough to
make an impact. Remember, King Fritz was just a human and his bloodline can be
diluted to the point where Ymir does not recognize it and all subjects are
connected through Paths so that can not be diluted. Only one of the 3
daughters was kept as the Queen of Eldia and kept the Royal Family bloodline
as pure as possible (possibly through incest, IDK. Historia was not a result
of incest so it is a bit confusing). The other 2 were used as breeding
machines to create more subjects of Ymir, diluting the Royal blood immensely.

