So Obey's Emlizy has made quite a showing with her in the support role. A lot of people in my casual games, throw up a lot of question marks or flaming opposition when I fill support with Amaterasu, considering it a troll pick. I'm here to not just provide "SPL player does the thing" but present it as an effective pick and why it works.
At level 1 you will start with Divine Prescence/Power Stance, build being watchers, boots 1, and health+ mutli-pots. I like to go 4/3 of each respectively.
Health and multis will be better for more aggressive positioning, allowing you to take poke better. Watchers will sustain your mana for the most part.
Why this over mirror at level 1? 15 physical power to both you and your adc applies bonus damage to wave, as well as Ama's Illuminating Strike passive, allows for decent clear. Movement speed is also good for disengaging you and your adc.
With power aura you get about 15 more damage an auto, and 12 more damage on the average 80% scaling hunter ability at level 1. While not as particularly strong clear as Sylvanus and Ymir, it's still a decent option for early game. Opting for the one also gives you sustain for poke as well as a movement speed disengage. 15 more damage an auto works very well on hunters like Rama, Apollo or Izanami that make good use of plain autos in the early game.
At level 2 you get your mirror which does 100 damage fully charged, as well as gives you a tiny 3% mitigation. This is very good compared to other guardian clear tools. Sobek 2/3 does 80/60 respectively as a comparison.
Level 3 obtains your silence/dash. This adds a little bit of control to your kit, albeit not as much as an Ymir freeze or Athena taunt. 70 base damage isn't bad either. Comparatively, Athena dash does 80 base.
Level 4 is another point in shield for clear/poke depending on how the lane is going.
At 5 you get an ultimate that does approximately a third of a squishies health, as well as gives a very good amount of zone control. Beads get popped for a potential 2s stun, and aegis if you don't want to take the damage. This ability is very strong into gods with no escapes like Poseidon, Zeus, or AMC.
What Amaterasu brings to the table
Movement speed: This is the biggest one. Rotational power is extremely strong, which is one of the reasons globals are valued so highly (Janus/Ratatoskr/Thor). The only other god that fills this niche consistently is Nike, who has it on a passive and in no degree as high as Amaterasu. This will let you take objectives faster, gank/counter-gank faster, allow you to disengage or re-engage, etc. Movement speed is extremely undervalued in terms of what its capable of providing for a team. Obey would make escapeless gods like Zeus and to a lesser extent Vulcan be more safe or get them to where they needed to be faster. In the support role this becomes even more effective. Ama in the support role means the movement aura can be utilized by your jungler and mid the entire game past laning phase, while a solo Ama would really only provide it in the mid to late.
Sustained tanking: The heal on her 1 combined with the mitigations on Ama's 2 make her a very difficult to kill frontliner. She heals 220+20% on about a 5s CD in the late game, which adds up big.
Free power: 15 scaling up to 35 bonus power is amazing for teamfights and objectives. Other gods that fill this niche are Nike and Fafnir, the former being a relatively late game passive, while Fafnir's is on an ult in order to apply it to the whole team.
Reverse Spirit Robe on enemies: 10% additional damage adds up late game by a ton. The low maintenance of its application (auto-attacks) makes it a really good passive to murder souls in the late game. Since it's an aura after 3 autos, and relatively easy to apply for 1 target.
Problems with Amaterasu support
Low control outside of ulti: Amaterasu's peel is sadly lacking in the CC department. A guardian/high cc assassin in the jungle or solo lane is recommended to compensate for the CC Ama lacks. High control midlaners like Nox also work, but note that the CC has to come from somewhere. Note that Obey comps ALWAYS had Maniakk run a guardian out of solo.
Early ganks/cc+clear gods: Ama's level 1+2 in the support role are not very safe due to the leveling of her abilities. Early ganks hurt a lot, or guardians whose clear tools also have CC on them like Ymir or Sylvanus do a very good job at obtaining pressure against an Ama supp lane because she has to respect their lockdown early. Displacement+lockdown lanes should be played carefully, like Sobek, Anhur, and Neith.
Enemy gods with a lot of self-peel: To get the most out of the ultimate, gods with low movement are better on the enemy team. Alternatively, a high cc god from the jungle or solo can force enemy escapes allowing you to get more value from your ultimate. Running Ama supp as a solo tank or as the only CC is problematic. Unlike gods like Khumbha, Ama can't apply enough CC for an entire team consistently and reliably.
Let me know what you think! I really hope this provides a pretty good overview on Amaterasu support and how it could be seen as a more viable pick in the right team compositions.