I'm not sure how much help this will be, because it's specifically about the "great" Rings of Power, and not the lesser rings (which there is just such scant info on). But Gandalf says something interesting about the Rings of Power (excluding the One):
Quote:
"The Nine, the Seven, and the Three, had each their proper gem. Not so the One."~The Council of Elrond
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Now we know the gems that adorned the Three. Vilya, had sapphire, diamond for Nenya, and ruby for Narya. The other Rings we don't know the gems, but it seems clear they would have been adorned with a gem.
Furthermore, with the Rings of Power (again excluding the One), Gandalf says "
proper gem," which suggests the gem was instrumental, or in some way an important factor in the powers of the rings. For example, Vilya, the Ring of Air, was adorned with a sapphire. Of Manwe:
Quote:
In Arda his delight is in the winds and the clouds, and in all regions of the air, from the heights to the depths, from the utmost borders of the Veil of Arda to the breezes that blow in the grass.~The Silmarillion: The Valaquenta
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More interesting yet, Manwe's sceptre:
Quote:
His raimant is blue, and blue is the fire of of his eyes, and his sceptre is of sapphire...~Of the Beginning of Days
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So, I think there are clear connections between the Rings of Power and gems. The great Rings of Power, specifically having "each their proper gem."
I don't want to tangent too far away from the lesser rings, but is it too much speculation to say whatever purposes the lesser rings were made for, the maker did not set in the "proper gem." Or perhaps no gem at all? Then again, the One has no gem, and it is the most powerful Ring of the bunch; being a simple band of gold.

I haven't the faintest clue where this leads the discussion, but I do think at least in ring-crafting (within the context of Middle-earth)...each having a gem is important to the rings' powers.