So, "every ring" is a pretty broad category and needs to be clarified before a good answer can be given. Most people assume magic rings, but not all the magic rings were known to be bound to the One Ring. However, we also don't really know what powers the lesser rings not bound to the One Ring were. Presuming magic still existed after the destruction of the One Ring, the non-linked lesser rings should still have powers, just maybe less in proportion to the overall fading of magic in Middle-earth.