The problem, though, is that it doesn't. The version of God espoused by many (both historical and contemporary) Jewish theologians distances itself from the problem of evil often by eschewing both the necessity of compassion and "omnipotence."
It may be a term that was invented by the religious right, but it still denotes a God with certain characteristics... particularly the characteristics the "Problem of Evil" uses as its core arguments.
Honestly, I don't give two shits if the religious right invented it because it has become a standard definitive term in philosophy of religion because it so clearly defines one particular version of God.
Keep in mind the word "omnipotence" is a Greek word, not a Hebrew one, and so it's not a concept that the Jews were aware of. Moreover, there's very little support for it in the text, and it's fairly easy to find counterfactuals in the [Jewish] Bible that don't support it.
The problem is that it puts Jewish theologians in the position of defending an image of God that the Christians inherit from Plato and Aristotle, which they have no desire to do.