I like the idea for the eye design, but every dojutsu thusfar has evolved from something established. Sharingan and Byakugan evolved from blood lines within the clan mixed with potential and skill. It doesn't seem that all clan members can obtain these dojutsus. Rinnegan evolution from sharingan when in the body of one that possesses senju and uchiha blood along with the skill/potential for it. Seeing as Naruto has no predicate indications of a dojutsu, a very thin theory. I will say that we still don't know the full history of the Uzimaki. They could be an ancient branch from uchiha and senju, but they were established before the village system so that's assuming alot. The Uzimaki are known for certain attributes such as vast chakra, stamina, and longevity, but no dojutsu abilities ever hinted towards, other than the transplant eye to Nagato. A transplant eye doesn't equate to much seeing as the sharigan and byakugan can be transplanted into other clans, even into their arms and be functional. As far as we know, Madara chose Nagato, an uzimaki, simply because he knew he had the chakra reserves to handle the power of the Rinnegan and was in a perfect situation to be manipulated, growing up in the hidden rain village.
