What difference did the Twelve tangibly make?

[Zero-ELEC]

Well, no, the Twelve aren't an Eorzea exclusive thing. The Twelve are arcane creations made of members of Venat's group (it's unclear if they're actually slivers of souls or just based on their souls), whose purpose was to ensure the world continued without breaking down, presumably because of the sundering. Hydaelyn didn't create them to "take people's desire to worship gods seriously" at all, I don't know where you got that.

Also the Twelve were summoned as primals, during the first Battle of Cartenau, even if only partially. Similarly, there was an Ascian plot to make Ala Mighans summon Rhalgr. Anything can be summoned as a primal.

Regardless, I agree that them being "actual" gods really adds little to the setting.