Question about founding titan and royal blood

First of all, ı am not a fan of series. I am just a casual reader of manga thus have limited knowledge. I apologize if my "theory" is stupid.

Now, we know someone needs royal blood to actually activate full power of founding titan. But when you think about it, every eldian is descendant of ymir and the king thus has royal blood. Now, we say "ymir must recognize them as royalty" for that to work but is it? How did ymir considered diana a royal family member then? What distinction did she have compared to others? At which branches does ymir stop considering a branch royal family?

So what if it isnt ymir who considers them royal family but themselves? By realizing the blood of first king fritz in their veins and considering themselves a "royal" would it be possible to open a line yo the paths? Like founding titan never got inhereted anyone other than one descendant line of ymir. Maybe its not that recognation of ymir as royal, but more like having sort of pride/acknowledgement of fritzs blood?