What I have offered is a logical argument for a plausible theory which answers the question posed by the OP: If God exists why does He allow suffering?
I will give you that, it is a plausible theory.
My argument supporting the claim that undue suffering is not necessary to motivate moral progress:
P1 If a Creator exists (conditional premise)
P2 We humans were created with free will and capable of both bad and good behavior.
P3 All suffering is not caused by bad behavior, as some suffering is not subject to free will, it is fated by God.
P4 There will always be suffering because that is inherent in the material world.
P5 Some suffering is part of the human condition owing to the material world which causes suffering.
P6 God adds to our suffering by determining a fate whereby people will suffer, some more than others.
P7 A world without undue suffering could still motivate change.
P8 We humans have been making moral progress.
C1 Therefore, it's possible that some suffering is necessary to motivate moral progress, but moral progress could still be achieved with less suffering than we see in the world at present.
C2 It is possible that God does not care how much individuals suffer, since there is no evidence of God's mitigation. Perhaps we are just a means to accomplish God's end.