Well, even though fallen angels/demons are not mentioned, they have always been in the world to deceive mankind and it was the same after Noah and his offspring began to repopulated the earth. Mankind has always been exposed to their temptations. However, during the thousand years, Satan and his angels will be locked up in the Abyss. So during the thousand years, mankind will not be exposed to the deceptions and temptations of fallen angels. It will not be of mankind's own accord, but will be due to Satan and his angels being released to influence mankind once again after a thousand years of peace.
It's not "some how they all go wicked," but because Satan and his angels will be released again.
God told Adam and Eve that in the day that they ate of the fruit of the tree of the knowledge of good and evil, that they would surely die. The serpent/Satan came along and said, "no, you will not die. God knows that in the day that you of it you will become like God knowing good from evil." So Eve believed what the serpent/Satan said instead of what God said. Since then, God has been looking for those who will believe in His word. Mankind always allows himself to be deceived and drawn away from God by the tempter and that is what is going to happen here after a thousand years of no temptation or deception, until they are let out of the Abyss, where at that time they will listen to Satan again and be drawn away.
Except for this time, there will be a large amount of people who believe in God's word and will hold tight to it, keeping the testimony of Jesus and not allowing themselves to be deceived and to be drawn away, which is the true church.