In response to “Would we be worse off without religion?” “No.” More than likely, very similar. I don’t think religion is the problem. Religion is the “Result.” If we did not buy into magical thinking and religious ideology it would be something else; Marxism, Socialism, Communism. There would be some magical belief system put in place that the ignorant could rely on for answers. And those that opposed the system would, of course, be banished to concentration camps or put to death. This is human nature.
Look at small ancient tribal communities. They make up their rules, invent their superstitions, and create their gods (which are different gods from the gods of the neighboring tribes.) Each tribe has its own rituals, taboos, and ritualized punishments for violating those taboos. (Not a lot different from many countries in the world today.)
Interestingly, there are documented cases of Atheist tribal communities. Unfortunately for us, these communities did not flourish.
In my personal opinion, religion is not the enemy, but rather, our own minds, our own gullibility, and our own willingness to accept magical thinking as an appropriate response to those things about which we know very little.
So, would a world be worse without religion? It would be the same. The reason it would be the same is that by doing away with religion you are only addressing the symptom and not the cause.
This is why I continually make the assertion; ‘Knowledge is the bane of religion.’ Knowledge may not be perfect as we are still very delusionally oriented beings, but it is the best weapon we have against the spread of myth and falshoods masquerading as that which is real. (That which is real is independently verifiable, measurable, and produces effects that are observable.)
IN SHORT: We are the problem. Not religion.