Sasuke claimed that Susanoō was the "third" power available to those who awakened the powers of both Mangekyō Sharingan. The discrepancies we've seen from both Kamui and Kotoamatsukami could have been due to the compatibility between users, and how they were developed, rather than the eyes themselves. Amaterasu and Kagutsuchi revolve around the creation and manipulation of Enton, but still have a distinct purpose; representing two cornerstones of chakra control.
Limiting Susanoō's invocation to this criteria would also explain it's supposed rarity, if Obito and Shisui's possession of a singular ocular power represented the more common result of those who awakened the Mangekyō Sharingan.
And it seems that the eyes are only necessary to "awaken" Susanoō, explaining why we've seen it materialized when the eyes have been blinded(Itachi), blindfolded(Sasuke), or missing entirely(Madara, as you mentioned).
Limiting Susanoō's invocation to this criteria would also explain it's supposed rarity, if Obito and Shisui's possession of a singular ocular power represented the more common result of those who awakened the Mangekyō Sharingan.
And it seems that the eyes are only necessary to "awaken" Susanoō, explaining why we've seen it materialized when the eyes have been blinded(Itachi), blindfolded(Sasuke), or missing entirely(Madara, as you mentioned).