Not killing and not stealing don’t need to be institutionalised for me to think they are good ideas. They might need to be institutionalised to protect me from people whose psychology lies outside that range along a spectrum that we call normal, but a government can do that. That churches and governments were once the same thing doesn’t validate your claimed utility of religion.
It is an interesting counter-factual speculation to posit that mankind could have organized and developed perfectly well without religion. It is impossible to re-run the experiment. Ultimately your argument is against the necessity of belief, not the utility. Christianity may have often been cruel, backward, and inefficient., but from a historical perspective- necessary or not- it played a role.
The fact that people are able to achieve power roughly equivalent to religious belief with fake science suggests that secular superstition might have worked as well. But, in the absence of scientific knowledge, or a widely established and accepted process of achieving it, power would inevitably flow to those who explained- convincingly if not accurately- how the world worked.
Criticizing the early parts of the Bible overlooks the fact that, to the ancients, religion and morality were not always the same thing. The Greek and Roman gods were self-interested and destructive. Most of the cults and ceremonies were practical and civic rather than moral. A god who turned himself into various animals to have sex with cute humans was not one that anyone looked to for moral instruction. The God of the Jews gave them laws, many arbitrary, but, as the story of Job illustrates, He was not bound by them. He could kill a man's family and cover him with boils just to win a bet.
But even if they were not part of the religion, classical cultures did have standards of morality. You could be jailed in pagan Rome for theft, or executed for any number of offenses. There were no real police, of course. Men of power had their own private armies and assassins. Government, law and religion co-evolved.
Separating them is an interesting challenge, but the best that can be achieved is smart, speculative fiction.