I'm going to go with the original poster and claim this as a plot hole. Every Subject of Ymir should be able to trace their lineage directly back to Ymir and the first King Fritz. Incest isn't mentioned and Fritz's last wish for his daughters was to reproduce as much as possible to pass down the Titan's power. This would mean the daughters would need to take "lowborn" husbands to pass on the bloodline. Again, incest isn't mentioned, so Fritz's grandchildren would also take commoners as mates (male or female), so forth and so on with every generation. With Fritz and Ymir as the progenitors for ALL subjects of Ymir and excluding incest (since it isn't mentioned), I can't think of a way for the royal bloodline to be so indistinguishable enough for the Founding Titan's power to be passed down only through a specific lineage. For all intents and purposes, every Ymir Subject is as much of a cousin to the next and any Ymir Subject should (theoretically) be able to use the Founding Titan's power. Unless it's passed down through the male lineage, but Fritz didn't have any sons. Unless it's passed through the female lineage, but what would make a daughter from Sheena more apt to the Founding Titan's powers than a daughter from Maria, since they are both direct descendents from Ymir/Fritz? Unless it's passed down through the Fritz's ruling line of succession, but that's just through a naming convention to where, if that were the case, then the FT's power simply follows a named successor (and that's just silly). Hmm, my last point may very well be the case of how the bloodline remains "distinctly Fritz" - in name only, I guess.