According to the poem:
Three Rings for the Elven-kings under the sky,
Seven for the Dwarf-lords in their halls of stone,
Nine for Mortal Men doomed to die,
One for the Dark Lord on his dark throne
In the Land of Mordor where the Shadows lie.
One Ring to rule them all. One Ring to find them,
One Ring to bring them all and in the darkness bind them
In the Land of Mordor where the Shadows lie.
This implies that the One Ring has power over the other rings and those that bear them. I'm not fully knowledgeable about the state of the other rings in the setting of the Lord of the Rings trilogy but I'm under the impression that nine rings were worn by the Nazgûl were already under the power of Sauron. The rings given to the Dwarves were lost, or Sauron had recovered them. The rings owned by the elves could have been destroyed or safely hidden so to avoid being used by anyone.
Why was it imperative that the One Ring be destroyed if its control over the other ring bearers would be negligible?