Board Thread:Naruto Discussions/@comment-34436445-20180703141210/@comment-1512913-20180705085441

As stated above, Kishi likely did this to give Sasuke sort of a pseudo-Rinne Sharingan. The tomoe in the Rinnegan eye is 100% just Sharingan active over it, but the mere fact that it's possible for him to have 2 doujutsu at once is special.

So while the Rinne Sharingan is the progenitor as both the Rinnegan and Sharingan come from it and it seemingly has powers of both (people will say that Kaguya never demonstrated any Rinnegan powers but I disagree, but that's for another topic) And so does Sasuke have powers of both in 1 eye, yet he doesn't have a Rinne Sharingan, just Rinnegan and Sharingan simultaneously, sort of a pseudo-Rinne Sharingan.

If you think about it, makes sense. The plot related reason why he wasn't given a proper Rinne Sharingan might be in case he never decides that he has a bad mood and it's time to enslave the entire world in a genjutsu to make himself feel better... a little prevention from wicked desires :D