don't feel like wading through 16 pages to see if this has already been mentioned

why no Odin? Because of how Odin exists in the lore of this game. It's nor a proper summon/primal but exists as a piece of cursed equipment. This is why every time you fight Odin in the shroud, it takes on the appearance of an actual player.

why no Shiva? Same answer, because of how the lore surrounding her summoning exists in the game. She required a human vessel to enable her summoning. This was true when Ysale invoked her in Heavensward and remained true when Rhyne invoked her on The First, and even there her influence was so strong that Rhyne had trouble controlling her.

I'd have preferred we get Alexander rather than a second Bahamut, but even then Alexander by the game's lore decided to deactivate himself to keep his power from being abused, so likely wouldn't be keen to answer our call to summon him