Interesting. This might be true. However itachi seemed to imply that madara was not the only one who awakened the EMS. Also Indra could have never awakened EMS since he was the only one with the sharingan at the time. That is unless he had a child and took said child's eyes.We can't really say whether obtaining EMS is a requirement or not seeing how no one has obtained the EMS except for Indra. I mean the Tablet said that Yin and Yang had to become one, but it says that only after the portion about attaining EMS. TBH, its possible that attaining EMS could also be something that only Indra can do. It could very well be a special bloodline selection much like Torune's micro bugs where only a select few in a clan can achieve. There being only one Indra just makes it really rare.
It could very well be that only Indra is able to reach the true height of the sharingan (EMS) and therefore only he can obtain the rinnengan. Logically speaking Hagoromo did give the tablet to Indra in the first place
Even if only Indra and his reincarnations could awaken EMS it still does not explain why they can only gain the rinnegan by stealing genetic material from ashura and his reincarnations. Why won't any of ashura's descendants do. Why only his reincarnations? This can only be so if the reverse is the case for example after defeating madara hashirama would take his eyes and awaken the rinnegan.
Another thing to note is that sasuke and madara both of which are indra's reincarnations do not share any close genetic connection besides both being uchiha. Therefore getting EMS cannot be considered a specific bloodline selection. This once again comes back to the question I asked.