Can you please provide some sources for legends and fiction that treat magic rings as trivial items, like D&D does?
Few treat magic rings as trivial items, but many treat them as items that anyone can use.
Several even treat rings as items that anyone can use in a limited sense, but only with time, knowledge and exposue does one gain access to the full array of their ability.
If you look at European legends, the concept of a ring or cloak that can make you invisible is fairly common, and shows up in Grimm's Faerie tales. In Plato's Republic, we find the story of the Ring of Gyges (an invisibility ring). There are also legends about rings that give one power over a particular being, like a djinn. (Once you lose the ring, however, your life may be forfeit...) Aladdin found the ring by which he commanded the djinn early on in his adventures...
Those legends provided the basis for JRRT's "One Ring" which anyone can use to make themselves invisible, but continued exposure to the ring...well, you know the story. AFAIK, the other rings mentioned in the story are magical and not limited by stature (though they were conferred upon Rulers, it was for tactical reasons, not limitations upon the rings themselves).
Similarly, the ability to use a ring (or lamp) of 3 wishes is not limited by one's social stature, power or other means of measuring "level."
Andvarinaut, the famous Ring of the Niebelungens from The Volsunga Saga and The Nibelungenlied, is magical, but its magic (beyond its curse) is never detailed. However, it passes from person to person quite freely, and without regard for stature.
The (real) Kingmoor Ring and the Bramham Moor Ring are inscribed with charms of healing and protection.
Of the less powerful rings, you can find some that merely make one more lucky, or makes one more attractive (such as in Thackaray's The Rose and The Ring).
While not technically a ring, a bracelet in CS Lewis' Voyage of the Dawn Treader turns a young boy into a dragon (and this is definitely a negative in the storyline).