I’m not sure what you’re asking here. Are you wanting an example of logically necessary suffering, or justified gratuitous suffering?
I think I see logically necessary suffering: It’s summarized in the observation, “Vice is its own punishment, pleasure its own reward.” To try to put forward an argument:
- God created an ordered universe where people have the power of free will.
- It follows that actions have ordered consequences.
- To exercise free will, agents must be able to achieve consequences that are within their power.
It then follows that logically necessary suffering can result. If you want to burn your hand, you can place it in fire and it will burn. Drinking alcohol excessively leads to hangovers. Fornicate enough and you’ll get an STD or crisis pregnancy. For most evil, suffering logically follows. These are examples of logically necessary suffering.
My problem, though – I suppose I should now address exnihilo – is when God chooses not to heal us. For example, parents mutilate the genitals of their children, which still regularly occurs to male babies in the United States through a practice conflated with Biblical circumcision, for example. It’s logically necessary for the child to suffer the consequences of the genital mutilation, but I don’t see that it’s logically necessary that God refuse to heal after prayer until death. When the child grows to understand reality, and prays to be healed, at that point it seems to me to go from logically necessary suffering to gratuitous (unnecessary) suffering if God refuses to heal.
However, Corrie ten Boom has a good anecdote about apparently gratuitous suffering in the book /The Hiding Place/, ghost-written by two who interviewed her. The point is that God may not explain why we suffer because we’e not capable of understanding it in this mode of existence, in this spacetime; but, if we are changed after death, or if at death we move into a different mode of existence, we may be able to understand it. (Her example was wanting to carry some burden as a child; her father refused; as an adult she understood why, and saw how as a child she couldn’t see from an adult’s perspective.) You’re right, if we only say this, it’s “begging the question” to defeat the problem of evil. However, as Jimmy Akin pointed out, if we know that God loves us, then, combining that fact with this observation, it does successfully answer the objection to point out that God likely has a reason that we don’t understand. (In other words, rather than say, “God has a good reason because God has a good reason,” we are instead saying, “God has a good reason because God loves us.” Of course, you must show or learn elsewhere that God does indeed love us.)