People expect leaders that are:
* strong * fair * capable * intelligent * loyal * available * caring * personal * decisive * on top of things * courageous
People who believe in God see that as a list only God himself could check off. That means we have an innate desire for a leader with the qualities of God himself. To the extent that people try to find perfect leadership in imperfect men and ideas, they will be disappointed. Pick literally any names: Bush, Obama, Trump, Jobs, Gates, Musk -- even Gandhi, Mother Teresa, Dr. King and Thomas Jefferson. So we become disappointed and move on to other people and concepts. Or we find God as He is, not just as we would imagine Him, and find peace in belonging to Him.
In a more personal take, I tend to be hard on my bosses and organizations; at times I have to remind myself to have reasonable expectations for human leaders.
(Or maybe you forget "real" in you list of leadership qualities?)
Anyway, on the off chance that you (or someone else) want a real answer:
* I decided to give God a shot and He proved himself. It's surprising the number of people that presume God doesn't exist without actually asking Him if He's there and if He cares.
* Christian theology makes a lot of sense. It provides for dignity and equality of all people. It provides for mercy and reconciliation and harmony. It provides for justice and protection of the downtrodden and wronged. It provides meaning for everyone regardless of ability or circumstances. It's simultaneously simple enough for anyone to grasp and deep enough to challenge our greatest minds.
Maybe that's not useful to you... here's a good talk Tim Keller gave at Google that can talk to it better than I can: https://www.youtube.com/watch?v=Kxup3OS5ZhQ
I'm curious. What does this response look like? I can't say I've ever seen anything which would seem to match this, and it's definitely a question I've wondered about when I was a kid falling out of a sense of faith.
That being said, the Bible does say that if a son asks for bread, his father would not give him stones. So if someone asks God to make it clear that He exists and cares, God could literally start talking out loud if He felt that was best. But that's not typically my experience. Personally, I've heard God speak through feelings of conscience, relevant scriptures, wise words from godly people, a change in my heart over the course of a prayer, or serendipitous circumstances.
I'll be honest, it takes a certain level of trust in God for any of it to make sense. If someone approaches God with a sneer, I wouldn't count on God responding. If your child or SO spitefully challenged you to prove yourself, what would you do? That being said, God has a habit of going above and beyond for me.
To you, perhaps. It's pretty patronizing and narrow-minded to write off the views of billions of people as "archaic". In fact, theism is so common that you'd have to be in some kind of bubble to not have any friends, colleagues, or acquaintances that are theists. I'm sure they'd be disappointed (if not offended) to hear you refer to their beliefs like that.
If you want people to keep their religion to themselves, you should really treat their beliefs with a modicum of respect. Otherwise, you're just being abusive.
But your main point is well taken; infighting, irrationality, hypocrisy, and other bad behavior are certainly not unique to religious groups. Humanity is a much more common factor than theism.
As well all know, deprecated does not necessarily mean obsoleted. That is deprecated can eternal lie, and with odd futures even faith may fly.
More like millenia. When your little neo-human tribe could be coerced as a group into attacking the nearby human tribe to take their women and eliminate them as competitors for resources, the chances that your genes would survive went up. Religion and general leader following were great tools for group coordinated action. Any mutations in the brain that benefited those group coordinated actions tended to survive and spread.
Religious propensity was a survival trait.
As long as you recognize that absence of evidence cuts both ways. Assuming physiological predisposition towards religion and strong leaders, it's also possible that the disposition developed because God actually exists.
What came first, religion or God? Can you prove that scientifically? I'm not sure you can.
In short, regardless of what any individual believes, to science itself, God does not exist (unless He ever made Himself testable in some form).
If you suppose the absence of supernatural factors, of course you cannot conclusively prove the supernatural. Any why does science assume there are not supernatural factors? Well, there are valid reasons, but to a theist that's merely a model of reality for the purpose of discovery and pedagogy.
But to take the premise as the conclusion is a logical fallacy. And on top of that, the underlying premise (assume only the physical and measurable exist) is a metaphysical premise and outside the purview of science.
Of course, my hours of simulation are playing chess, Risk, Warcraft, and numerous other games -- but there's a reason those concepts are so often the core of games: they parallel real life and our desire to win at life.
Even modern psychology is fairly light on things that are proven. Insisting on proof to discuss psychological origins that we can't really test on real proto-humans before we even discuss it is just an attempt to shut down unpleasant ideas, like the idea that most religious beliefs are myths.
Growing up in a strong religious culture (though not a cult) that I later became disillusioned with, it almost hurt noticing the same trends in so many other areas of life that one would think immune from it. From sports to academics to social movements.
There is something inside of humans that has for centuries made religion very popular. Even now that many have been able to leave religion behind, what ever that is deep inside of use still exists and it is influencing the new social groups we form, creating systems of beliefs and rituals.