The Susano'o is a Mangekyou ability that operates on different rules than the rest of the Mangekyou abilities.
Firstly, Susano'o isn't a user-unique ability like Kamui, Amaterasu, Tsukuyomi, Kotoamatsukami, etc. Susano'o is the "everyone gets one" ability of the Mangekyou.
There is, however, one precursor to gaining the Susano'o: one must awakened Mangekyou Sharingan in both eyes. It cannot be awakened with just one eye, so a one-eyed Uchiha is out of luck and they won't gain Susano'o. That's why Obito is the only Uchiha we don't see use the Susano'o for the duration of the series (until he gets to the afterlife, but that's a complicated exception that I'll explain in another chapter so disregard Obito's Susano'o for the time being), not because he doesn't want to, but because he can't. He only awakened Mangekyou in one eye (with the other being in Kakashi's possession), so he didn't get Susano'o.
Furthermore, Suaano'o is the only Mangekyou Sharingan ability that is granted not to the Sharingan eyes, but to the user himself.
Susano'o is a non-transferable ability awoken within the wielder, not the eyes. Anyone can use Kamui, Amaterasu, Kotoamatsukami, etc. so long as they have those eyeballs with that power in their possession. But you can't gain Susano'o from eye swapping. It is a Sharingan power, sort of, but not a transferable one. Which means that it is impossible for anyone not of the Uchiha bloodline to use the Susano'o.
And I say this because:
1. No one except the Uchiha ever uses the Susano'o, not even people like Danzo or Shin who had the Mangekyou Sharingan used Susano'o.
2. Madara didn't need any eyes at all to use Susano'o.
Susano'o is an intrinsic ability to any Uchiha user who has awakened MS in both eyes. Which means that even if an Uchiha's eyes are destroyed, they can still use Susano'o. That's also why although it's claimed that both eyes are needed for Susano'o, they are only needed for the initial awakening. After the initial awakening of the Mangekyou Sharingan, the Susano'o ability is unlocked, and from then on a user can always wield Susano'o anytime with or without his Sharingan. That's why Shisui had no trouble using his Susano'o with a single eye after his other eye was stolen by Danzo, why Madara was able to use Susano'o even without any Sharingan at all, and why in his final moments Itachi could sustain the Susano'o without his Mangekyou Sharingan being activated.
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That's also why Sasuke doesn't always have his Mangekyou Sharingan turned on when he uses Susano'o: because he doesn't need it, because the Susano'o is an ability that is always available to its user, regardless of whether their Sharingan is activated or not, or regardless if they even have any eyes at all.
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Besides, Sasuke later swapped his eyes for Itachi's eyes so that Sasuke could awaken Eternal Mangekyou Sharingan, and his Susano'o remained purple, just the same as before when it was only his own eyes. So it appears that one's Susano'o colors do not change even when one switches eyes, and it's another sign that the Susano'o is a nontransferable ability.
Susano'o is unique in this, because not only is it the only nontransferable Mangekyou ability, it is also the only recurring common Mangekyou ability that all those who awakened Mangekyou Sharingan in both eyes can expect to have access to.
