It is interesting to compare these verses to what came about in the premortal world.
Revelation 20:1 And I saw an angel come down from heaven, having the key of the bottomless pit and a great chain in his hand.
2 And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years,
3 And cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till the thousand years should be fulfilled: and after that he must be loosed a little season.
In the premortal world, there was a great war that now continues here. It is clear that the adversary had a great deal of time to sway men there before being cast out, or how could he have obtained a full third of the Father's children. But in the end, he was cast out.
And it is interesting that we see something similar here on earth.
Yes, Satan will be bound by the righteousness of the people, but it will still happen as described in the above verses. One would guess that when there are righteous enough people then, as during the war in heaven, Satan will be cast out by the power of the priesthood. And in turn, that will replace war with an age of peace, just as it surely did in the premortal world.