Punishment actually has a range of meaning. It could simply refer to the natural consequences of an action as in Romans...
Romans 1:27 Likewise also the men, leaving the natural use of the woman, burned in their lust for one another, men with men committing what is shameful, and receiving in themselves the penalty of their error which was due.
Then I understood you correctly.
If there is a goal it is to serve justice.
Romans 1:32 who, knowing the righteous judgment of God, that those who practice such things are deserving of death, not only do the same but also approve of those who practice them.
Luke 12: 47 And that servant who knew his master’s will, and did not prepare himself or do according to his will, shall be beaten with many stripes. 48 But he who did not know, yet committed things deserving of stripes, shall be beaten with few. For everyone to whom much is given, from him much will be required; and to whom much has been committed, of him they will ask the more.
And there is a deterrent effect as well...
Where there is no fear of God there is no deterrent effect....
Genesis 20:11 And Abraham said, “Because I thought, surely the fear of God is not in this place; and they will kill me on account of my wife.
Where the fear of God exists, the deterrent effect also exists...
Exodus 1:17 But the midwives feared God, and did not do as the king of Egypt commanded them, but saved the male children alive.
Seems pretty straight forward to me. Where is there room for controversy?
As for Hell itself being a punishment, what I said before I say again....
The wages of sin is death. That makes sense because God is life itself. That which is proper to life is the good; that which negates, opposes or destroys live is the evil. Thus, the wages of sin is death because it is the seed of death. Sin is death in its nascent stage. Death then isn't any more (or less) of a punishment for sin than is sitting in the dark a punishment for turning off the lights.
When people go to Hell for rejecting God and His offer of salvation through the death of His Son, God is only granting them that which they have desired, which is to be away from Him and forever so. Since God is Life, being separated from God is the very definition of death, at least in the spiritual sense of the term.