Why is There A Hell?
There is a hell because God wants as many as people in heaven as possible. See Case for Faith, page 188-189.
There is no contempt in a soul that ceases to exist, but there is in hell. Those who go to hell are intrinsically valuable people made in God's image. C.S. Lewis wrote the doctrine of hell is "one of the chief grounds on which Christianity is attacked as barbarous and the goodness of God impugned" (The Problem of Pain).
"Multitudes who sleep in the dust of the earth will awake: some to everlasting life, others to shame and everlasting contempt." (Dan. 12.2).
Everyone is going to be resurrected, whether to everlasting life or everlasting contempt. Everlasting existence is the same everlasting either way, only the destination is different. Ceasing to exist is not an everlasting, nor is the resurrection of the damned to lead to annihilation. God is not going to resurrect the unsaved then annihilate them.
J.P. Moreland says the flame language is figurative. Death put to an end is because there will be no more death, so the everlasting flames in punishment is meant as a figure of speech for judgment and eternal separation, not a literal burning. In Heb. 12.29, God is called a consuming fire. Yet nobody thinks God is a cosmic Bunsen burner. Flames pertain to God's judgment.