Sasuke doesn't even have hashirama's genes, his rinnegan was the result of hagoromo's chakra via his yin portion with that massive amount of chakra mixed with indra's chakra, it created a Tomoe rinnegan.
Also the answer is extremely obvious, Naruto has RSM since the sage gave him his yang portion plus Ashura's influence along with the bijuu, Naruto could get a rinnegan by mixing uchiha genes but it would be vastly inferior to Sasuke's just like if sasuke got sage mode it'd be vastly inferior to naruto's, reasoning being that Tomoe rinnegan is equal if not greater than regular rinnegan and sasuke has EMS on top of that. Sasuke could get RSM by having his own sage mode first but it will not be on the same level as Naruto unless he absorbed all of hagoromo's yang chakra from Naruto otherwise with just the same portion of the nine bijuu as Naruto had with sage mode it won't be RSM level without hagoromo's yang.
Naruto and Sasuke shine with their own respective abilities it isn't plot that doesn't enable them to have it...it's basically common sense, Naruto isn't about to bite sasuke like madara did to hashi to get some Indra chakra or dig up Madara's grave for it, and sasuke's not about to have Bijuu Open Season, it's unnecessary really they're already strong enough the only thing that's plot is sasuke not having an arm but I guess unlike past Uchihas he doesn't want to get high on hashi genes :Sparks:
