Why the devil is still around to tempt man and not eradicated from the first only by God?

By tempting Adam and Eve, the devil brought up the question of God's right to Sovereignty over man. If God had just destroyed him and his followers, that question would not have been answered. It would have been much easier for God to just destroy those gone astray and start over, but in order to prove His right as Sovereign Lord He has allowed Satan to run amok (so to speak) and when the time is right, God will do away with Satan and all those who have chosen to follow him instead of sticking beside God. Also, Satan has also stated that mankind will only follow God if it is to their benefit and would turn their backs on Him if it is not so. God has given Satan a chance to try and prove both these claims until the day it is proven otherwise. See the example of Job on the latter point.