This is a key plot point: <PERSON> never even thinks of the possibility that the <PERSON> will try to destroy the <PERSON>. He cannot imagine somebody voluntarily giving up that much power. From the book:
<PERSON>: For he is very wise, and weighs all things to a nicety in the scales of his malice. But the only measure that he knows is desire, desire for power, and so he judges all hearts. Into his heart thought will not enter than any will refuse it, that having the Ring we may seek to destroy it. If we seek this, we shall put him out of his reckoning.
After the Fellowship split, <PERSON> and <PERSON> work hard to maintain this deception. They want <PERSON> to believe that <PERSON> has the Ring.
When <PERSON> uses the Palantir at Isengard, <PERSON> sees a hobbit for a few seconds. He thinks that <PERSON> has captured the Ringbearer.
After <PERSON> is destroyed, <PERSON> uses the Palantir to taunt <PERSON>. From that moment, <PERSON> believes that <PERSON> has the Ring.
<PERSON> then does exactly what he knows <PERSON> expects him to do if he had the Ring: raise an army and march to the Black Gate to make a frontal assault on Mordor. This was a terrible risk, taken to keep <PERSON>'s attention and forces focused on <PERSON>.
And note one more point: <PERSON> was right. Nobody could voluntarily destroy the Ring. 773
When the time came to throw the Ring into the fire, <PERSON> could not do it. If <PERSON> had not been there, <PERSON> would indeed have succumbed to the <PERSON>'s temptation and tried to wield its power.
In a letter to a reader, <PERSON> described what would have happened next. <PERSON> would have immediately sent the eight surviving Nazgul.
I think they would have shown 'servility'. They would have greeted <PERSON> as 'Lord'. With fair speeches they would have induced him to leave the Sammath Naur [Mount Doom] - for instance 'to look upon his new kingdom, and behold afar with his new sight the abode of power that he must now claim and turn to his own purposes'. Once outside the chamber while he was gazing some of them would have destroyed the entrance. [...] In any case a confrontation of <PERSON> and <PERSON> would soon have taken place, if the Ring was intact. Its result was inevitable. <PERSON> would have been utterly overthrown: crushed to dust, or preserved in torment as a gibbering slave. <PERSON> would not have feared the Ring! It was his own and under his will. <PERSON> Letters 246 381