I dont think Hylia is based on Amaterasu. Please provide evidence - either actual game writers evidence or at least your reasons why this symbolism exits. Hylia is a goddess associated with light and maybe creation (though there is another goddess for that sometimes), it can be linked to the sun because that is basic human thinking sun=light=life source. But, for a link to Amaterasu there needs to be a reflection of Amaterasu's story elements or typical items. E.g. going into a cave or being the origin of agriculture.

In my opinion the three deities also are way more even than Zelda - Link - Ganon are. In your arguments, Link and Zelda and Ganon would be siblings of about equal power level with Zelda slightly above. I think Skyward Sword clearly positions Demise as an equal to Zelda but of different origin and Link as a chosen one (others exists).

What about the current BotW/TotK where Ganon is controlling the blood moon?

You admit that the other two associatinos for Link and Ganon are loose. The Moon children are on the Moon because the Moon was made by Majoras Mask. So, with the blood moon, this is now the second time, the moon is associated with the game' "evil"/"corrupted".

The rabbit imagry in a link to the past and repeated in link between worlds is because fear is the opposite to bravery. This is explained in both games.

The wolf is not associated with the moon in Japanese folk lore as far as I am aware? (I understand your association, but it stems from werewolve and north european ideas, such as fenrir chasing and eventually eating the moon).

Also, a minor nitpick, but being able to throw lightning does not mean you are the god of storm. Link also controls lightning various times, Urbosa does as well.