: The Rings of Power were originally intended for the Elves and the Elves alone. They never even divulged the existence of the Rings to their closest allies (the Numenoreans) until the time of the War of the Last Alliance, after the Downfall of Numenor.

That might have been from embarassment since they got "hoisted by their own petard"

: The associations by kindred (three for the elven kings, seven for the dwarf-lords, nine for mortal men) were a purely poetic invention of the composer of the Ring-rhyme, which preserved a memory of what happened to the Rings after their dispositions had been determined (probably when Elendil and Gil-galad formed their alliance -- I can't see the Dwarves telling anyone they had Rings of Power until they were informed what the fuss was all about).

But the last sentence of the ring rhyme was carved into the One Ring. One of three things happened: either Sauron went back to the Sammath Naur and inscribed the Ring later; or, since he was involved in the making of the generic rings of power, he had already preplanned their hidden purposes; or the last sentence of the ring rhyme was a quote from Sauron's "spell" and the prior lines were simply added by some later author.

Russ