Actually since both Naruto and Reincarnation are fiction, reincarnation works however Kishi decides it works.
And Kishi is using the Reincarnation from classic eastern religion which is one soul being reborn over and over again.
The Six Paths of Pain are a direct reference to the Six paths of reincarnation.
Kishi basis his work off of Eastern religious and cultural stories, more than likely he will stick to the old story.
Besides Hashirama and Madara don't meet the criteria, Hashirama was a natural born genius and Madara lived in his shadow and respected him.
The Younger Son and Elder Son are the complete opposite, Naruto and Sasuke follow this to the letter.
Ashura is a talentless guy who made it to the top through hard work, Hashirama was born at the top.