Destruction of the The Ring...

[Tharlionglin]

I believe that when the ring was destroyed and Sauron, lost a hold of his physical form of the eye, he rose as a cloud of darkness and was blown away by a wind from the west, but I'm not a 100% sure.

My feeling is that like blowing a pile of sand out of your hand you cannot see the sand and where it lands but it is there none the less. Although not a focused entity, the evil that Sauron put into peoples hearts was still there none the less.

Even if Aragorn hunted down and slayed each and every creature touched by Sauron before his demise, the taint would still be created anew by the blowing of his darkness in the world.

Perhaps this is the will of Iluvater that nothing remains unsullied, including Valinor, and nothing is completely evil anymore either. The peoples of Middle-Earth had seen plenty of both, and been influenced by both, and now have the choice to make themselves.