I had the thought that the ring might actually be for "marriage" between a woman and a Great One after writing the post, too, which would explain why only one ring is necessary. That might even be why Arianna and fake Iosefka both fail to bear children for the Great One impregnating them (most likely Oedon); because the children were conceived "out of wedlock" (arguably Arianna did complete her pregnancy, though I'd still argue that the child was a failure since it, even after its birth, apparently remained directly linked to her lifeforce).

About Annalise (Annalise, Arianna, Amelia, Adella, Adeline... Bloodborne really likes its feminine names starting with "A"), it still seems significant to me that the player can use the ring to propose to her (regardless of the player character's sex), regardless of how special the player is, simply because they know that it is a thing. Whatever the player was when encountering Annalise they were originally a relatively mundane foreigner, so the only way they would know about the concept of marriage (barring magical knowledge gained from the ether upon picking up the item) to propose to her would be if it was something most people know about. Of course, knowing about something and being allowed to do it is two very different things...
The angle about eugenics does sound very interesting, though.

Extra: Digging some more, I discovered the existence of "official" Bloodborne comics that, as the [i]only[/i] IC source, has a woman - a commoner, no less - referencing her "husband", strongly suggesting that they were married. I can't find any reliable source that these comics are [i]official[/i] official to the extent that they would be a suitable basis of lore speculation, but it's something.