I've heard some answers on the Internet regarding to this topic:

1. Because Sasuke awakened a Rinnegan with 6 tomoe, which is equal to if not more powerful than a normal pair of Rinnegan


2. Because Sasuke only received half of Hagoromo's chakra

Neither of these make logical sense. (1) just says that his Rinnegan is more powerful, which proves nothing about why it cannot be doubled. (2) doesn't work because Madara got just a single piece of Hashirama's flesh in his wounds but he eventually still managed to awaken 2 Rinnegan at the same time.

Well firstly, the Uchiha themselves do not have the physical rigour to utilise both of the Rinnegan. Obito, who was deemed by Madara as his best substitute, explicitly state that he was unable to handle implanting both.

The only reason why Madara could handle them is due to Hashirama's cells. If he were to be in Obito's position, even Madara couldn't handle both Rinnegan. Sasuke, without any form of Senju/Uzumaki DNA within him, can't either.

So what happens if Sasuke was given Six Paths chakra, but his body couldn't handle the rigour of awakening it?

Now we know that two Rinnegan requires both the Sage's (or Indra's) eyes and the Sage's (or Ashura's) body to be used. So it's not too far fetch to say it also need both to even awaken. And since Sasuke receives Six Paths chakra from his left hand, naturally his left eye will be the first to awaken the Rinnegan.

Alternatively, Hagoromo may have already know this, so he likely perform some trick that prevents Sasuke from awakening both and die because of that. He has researched about how to release Infinite Tsukuyomi, so I don't see why not.

As for why only his Rinnegan has tomoe, that is a little harder to derive. Sasuke is the only one who awakened the Rinnegan through artificial means while Hagoromo and Madara awakened it naturally. Perhaps that is the factor that changes things but we will never know for sure since there is literally a sample size of 3 to compare.

And since we are here I want to clear up one more misconception. Sasuke's left eye is clearly a Rinne Sharingan. I only mention it as a Rinnegan to reference the Rinnegan aspect of it. For those who says its just a Rinnegan because:

1. It's purple


2. Hagoromo and everyone calls it a Rinnegan


3. It is not on his forehead


4. Naruto Wiki classifies it as a Rinnegan

Then tell me what eye is Urashiki's one ^. It's red, but Gaara still refers to it as a Rinnegan??

Momoshiki's eye is on his forehead, but no tomoe. Is that a Rinne Sharingan?

Sasuke can teleport and open portals, Kaguya can teleport and open portals, Urashiki could open portals???

But Momoshiki couldn't??? There is no denying this anymore.