I think one has to make quite a logical leap to go from rejecting eternal suffering to believing that doing so necessarily entails allowing "evil" or "sin" (by which you mean undesirable/negative things, I assume) to continue existing or spreading.
• If the supernatural entity in question has the ability to create a place of unimaginable suffering as well as a place of unimaginable bliss for certain people to eternally abide in, then I don't see why it is unreasonable to ask why that entity doesn't prevent evil and sin from occurring in the first place. Why go through that extra step of setting up a vast, detailed realm of suffering as a deterrent to "sin" when any undesirable action can be prevented without breaking a sweat? It seems to me that the purpose of eternal suffering wouldn't be rehabilitation or prevention of harm; it would be revenge.
• I think the idea that eternal suffering exists to prevent evil, sin, etc., from spreading contradicts itself, at least in the more common Christian versions thereof. All of the descriptions of eternal suffering I have read and/or heard about tend to involve judgment of people after they have committed actions that are perceived to be undesirable, such as harming another person. Those descriptions also tend to emphasize the helplessness of the people being judged, so it's clear that they can't cause further harm or "sin" anymore.
Put differently, who is being protected when everyone will supposedly be facing their final judgment where nothing will affect them except an omnipotent deity's will? And what is being prevented when everyone will supposedly be helpless and at the mercy of an entity that is infinitely more powerful than them? As I said above, I think that such concepts describe punishment whose purpose is revenge rather than anything else.
• Even if we assume that suffering in a lake of fire or any other place of torment is necessary to prevent harm, that still doesn't explain why it would have to be eternal. Why shouldn't "evildoers" be made to become permanently nonexistent, for example, or even be punished for a period of time before being transferred to a place of bliss or at least being made nonexistent? The imposition of an everlasting penalty on them doesn't seem to make more sense as a method of punishment or reformation than the employment of a temporary penalty to that end.
Considering the time period in which the Bible was written, I think most of the grotesque and vivid descriptions of suffering, fire, torment, etc., were primarily inspired by tribalism and sectarian zeal rather than any sort of revelation or divine guidance. I also find it disappointing if not downright scary that so many people still adhere to beliefs that teach that it is perfectly acceptable to see someone else experiencing unimaginable pain, know that they will be in it for eternity, and be happy about it and even view it as a sign of a particular deity's power or glory. That's one of the areas in which I think humanity still has a lot of progress to make.
