Because contrary to your assumption, the Ring could be used by other people
As said many times throughout The Lord of the Rings, and in Tolkien's letters, Sauron was afraid that his enemies would use the Ring against him, usurp him, and take his place as ruler. Not everyone would have the necessary will power to master the Ring, but some, like Gandalf and Aragorn definitely could. The main reason the Wise did not do this is because doing so would corrupt whoever used the Ring, and you would just replace one dark lord with another dark lord.
‘But I have so little of any of these things! You are wise and powerful. Will you not take the Ring?’
‘No!’ cried Gandalf, springing to his feet. ‘With that power I should have power too great and terrible. And over me the Ring would gain a power still greater and more deadly.’ His eyes flashed and his face was lit as by a fire within. ‘Do not tempt me! For I do not wish to become like the Dark Lord himself. Yet the way of the Ring to my heart is by pity, pity for weakness and the desire of strength to do good. Do not tempt me! I dare not take it, not even to keep it safe, unused. The wish to wield it would be too great, for my strength. I shall have such need of it. Great perils lie before me.’
The Lord of the Rings - Book I - Chapter 2 - "The Shadow of the Past"
In the forward to the second edition, Tolkien even presents us with a hypothetical scenario where the Ring was used against Sauron, and he tells us the outcome.
The real war does not resemble the legendary war in its process or its conclusion. If it had inspired or directed the development of the legend, then certainly the Ring would have been seized and used against Sauron; he would not have been annihilated but enslaved, and Barad-dûr would not have been destroyed but occupied. Saruman, failing to get possession of the Ring, would in the confusion and treacheries of the time have found in Mordor the missing links in his own researches into Ring-lore, and before long he would have made a Great Ring of his own with which to challenge the self-styled Ruler of Middle-earth. In that conflict both sides would have held hobbits in hatred and contempt: they would not long have survived even as slaves.
The Lord of the Rings - "Foreword to the Second Edition"