Recently we see some characters(Madara,Tobi, Danzo etc..) stealing senju and uchiha dna to gain the so6p's powers. Tobi even called himself the 2nd coming of the so6p even though his life mission resembles more the so6p older son getting revenge on the so6p's younger son like Madara.
The point I'm trying to make, is hertiage by genetics the true so6p successor like Madara and Tobi believe? If the so6p was looking down on Madara and Tobi now would he consider them a part of his legacy given what they have done and doing now?
What about following in the so6p's footsteps like Jiraiya? What would the So6p think of Jiraiya's efforts? Would the so6p think of Jiraiya as the son he never had?
What we haven't seen is the unification of the two ideals or have we? If the so6p's sons united instead of becoming enemies then battles/wars wouldnt have broke out in the shinobi world achieving peace, something the so6p would have wanted. At the end of the Nagato vs Naruto fight both representations of the so6p sons impraced Jiraiya and Nagato become the destined child along with Naruto in the end.
Jiraiya may not have bloodline limits like so6p; Nagato and Naruto aren't brothers; but we can see between the three of them what could have happened between the So6p and his sons if they joined forces in the end like Jiraiya's pupils. But I tell you what since both Naruto and Nagato are from the Uzumaki clan that gives them a genetic connection to one another the same as so6p's sons further coorelating the two.That's why this correlation is so intresting.
It’s said(by a couple of characters Jiraiya, shikamaru,Thrid hokage etc..) a student inherits his master's will despite not genetically related, we have seen many examples of this in Konoha with Jiraiya /Naruto and Asuma/Skikamaru. Madara and Tobi may have the so6p's body parts but they certainly don't have his will. Jiraiya is the true successor of the so6p in the narutoverse.