That's close to the argument, but it doesn't include line 1. Just drop the first line and start with line 2. The ancient Greek philosopher Epicurus framed it thusly:
"Is God willing to prevent evil, but not able? Then he is not omnipotent.
Is he able, but not willing? Then he is malevolent.
Is he both able and willing? Then whence cometh evil?
Is he neither able nor willing? Then why call him God?"
These are arguments that if a god exists, it isn't omnipotent, omniscient, and omnibenevolent.
Here's a more modern formulation of the same argument from Sam Harris that looks a lot like your line 6. Notice that neither of these quotes is an argument for atheism. They're arguments against the existence of a tri-omni god:
"Either God can do nothing to stop the catastrophes, or he doesn't care to, or he doesn't exist. God is either impotent, evil, or imaginary. Take your pick, and choose wisely."
And this is a theodicy:
"Theodicy means vindication of God. It is to answer the question of why a good God permits the manifestation of evil, thus resolving the issue of the problem of evil. Some theodicies also address the evidential problem of evil by attempting to make the existence of an all-knowing, all-powerful and all-good or omnibenevolent God consistent with the existence of evil or suffering in the world."
Here's an excellent example of the difference between critical thinking and faith-based thinking. The reason and evidence path looks at the problem of suffering to serve no apparent purpose, looks at the three statements, and declares them mutually exclusive and therefore logically impossible, just as a married bachelor is logically impossible because one can be either married or a bachelor, but not both at once in the same sense. And so, the critical thinker eliminates these possibilities from further consideration. There can be no tri-omni god in a world where there is so much grief and suffering.
But the faith-based thinker starts with the assumption that this impossible god exists, and tries to reconcile the suffering with the existence of the tri-omni god.
Yours is an example of Divine Command Theory, which posits that whatever the deity says or does is moral, and so, somehow, the coexistence of a tri-omni god and suffering is moral. Somehow, it's not gratuitous suffering - it's deserved, or it's constructive and salutary as you suggest. The danger here is coming to conclusions like yours that somehow, permitting suffering is good. Maybe you've seen Mother Teresa's take on that:
"There is something beautiful in seeing the poor accept their lot, to suffer it like Christ's Passion. The world gains much from their suffering." and "You are suffering like Christ on the cross. So Jesus must be kissing you."
If you can't see the danger in that kind of thinking, recall that she headed a series of hospices, whose mission is ordinarily to ease suffering, not to praise it as a gift from God.
The only suffering that it is moral to cause or permit is for constructive purposes, like giving a child a vaccine, or going hungry to lose weight, or clipping your dog's nails if he hates it. Causing or allowing a child to acquire and die of leukemia is immoral.
This is from the call-in cable show The Atheist Experience:
"You either have a God who sends child rapists to rape children or you have a God who simply watches it and says, 'When you're done, I'm going to punish you' .. If I were in a situation where I could stop a person from raping a child, I would. That's the difference between me and your God." - Tracie Harris
She thinks critically, and let's reason take her to it's inevitable conclusion - this god, if it exists, is immoral. Then the Christian caller says,
"True to life, you portray that little girl as someone who is innocent. She's just as evil as you."
He did what the Bible writers did. If God did this to her, she had it coming. If man must walk the earth scrounging for a living, it's because he deserves it thanks to Eve. Noah's contemporaries were all evil except him and his family, so they deserved the flood. The denizens of Sodom and Gomorrah must have been evil if they went extinct. And this caller says the same thing - if his good God allows a child to be raped, it must have deserved it.