The doctrines of eternal reward and of election and the study of spiritual beings (angelogy) require a doctrine of hell. Jethro Bodine stated it eloquently above.
Since we are created as free moral agents, we are thus free to reject what God has already provided. Eden provides us with many examples. foremost was the act of disobedience of Adam and Eve. they had daily contact with God, and everything was perfect in Eden. By choosing to question God's wisdom, and not obeying God, they lost Eden, being forced to leave it.
Then there was the fall of Satan. His rebellion took 1/3 of the angels with him because they refused to believe God, but followed jealous Satan instead.
Finally, since Eden was an earthly reflection of Heaven there must be a place for both the angels who lost their first estate as well as those who reject the clearly visible things of this world, which point to God.
Romans 1:18 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who hold the truth in unrighteousness;
19 Because that which may be known of God is manifest in them; for God hath shewed it unto them.
20 For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse:
21 Because that, when they knew God, they glorified him not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened.
22 Professing themselves to be wise, they became fools...
And because a refusal to believe is a rejection of election whereby man is saved by grace, (this is not promoting universalism) Hell must be the result of what happens when people choose to NOT listen to the things of this world that are all pointing to Jesus Christ for redemption.
Romans 1:28 And even as they did not like to retain God in their knowledge, God gave them over to a reprobate mind, to do those things which are not convenient;
29 Being filled with all unrighteousness, fornication, wickedness, covetousness, maliciousness; full of envy, murder, debate, deceit, malignity; whisperers,
30 Backbiters, haters of God, despiteful, proud, boasters, inventors of evil things, disobedient to parents,
31 Without understanding, covenantbreakers, without natural affection, implacable, unmerciful:
32 Who knowing the judgment of God, that they which commit such things are worthy of death, not only do the same, but have pleasure in them that do them.
So now you have my ideas, wrapped in Scripture why the doctrine of eternal punishment is important. it is not that God placed rebellious mankind in hell is is because people reject God, are unforgiven sinners, and the holiness of God is such that He cannot dwell in the presence of sin, that only the forgiven sinners, covered by the blood of Jesus Christ can enjoy the presence of God forever.