I'm not sure we have any societies, untouched by religion, to compare with.
It is true that the Judeo-Christian religions used religious law as a substitute for civil law. Christianity was born, nourished and matured under the society established Roman Empire. In any case there is no denying that these religions have bestowed great suffering upon the world over the past 3000 years. We can speak of what might have been but this is what really is.
You are correct that it is almost universal for humans throughout history to invent religions that explain the unanswerable questions of life nad give life meaning. Of course, every culture invents a different God, no two of them the same, and therein lies the rub.
Even the most devout extremist religious nut only has a small chance of having grown up being exposed to the "right" God/religion out of the thousands that have existed. You might actually be making the right God more angry by following a competing God than by choosing to stay on the sidelines and follow no God. But most religious people think that everything they believe is so blindingly obvious...