For most people, God is an imaginary belief, similar to cartoon fantasies. People have been trained to think that way and to behave on the basis of various fictions, externally imposed narratives, and lies, rather than taking the time to gather reproducibly experiencable facts and empirical evidence.
Then when they realize they can't rely on the fictional abstractions they have been indoctrinated to believe in, some join the religion of atheism, which is just another set of beliefs having nothing to do with Real Reality. Others abandon, or feel abandoned by, their faith. An therein lies the root of the problem: belief in intellectual abstractions and lies, rather than direct personal experiences.
The root of these kinds of problems is the thousands of years of enforced indoctrinations inculcated into the people by the various religious beliefs, and political persuasions, designed to control the actions and reactions of the masses of the populace, so the people give the ruling classes of the various religions and other imaginary political bodies, all their money and power and devotion.
This has been done through psychological manipulations which all have the basis of progressively removing people from the actual facts, removing them from having direct experiences and removing them from their senses and sensitivities, using intellectual abstractions, imaginary concepts, fictions, and lies, as the primary behavioral leverage.
And as you say, people are trained and "bound by blind conviction of logic and analysis". Logic does cause blindness to Real Reality and weakens the very senses and sensitivities which can bring each person to have personal experiences of Divinity.
When you are doing a math calculation, what happens to your senses? They are gone! (except for a tiny left-over bit of sensory awareness). When you are imagining things, what happens to the senses? They take leave of your awareness.
So to be "out of your mind" is a good thing, indicating sanity, rather than the insanity of the intellectual narrative that is always controlled by external interests, rather than your interests.
The old saying, "He's taken leave of his senses!", is exactly correct definition of insanity.
The correct definition of insanity is the loss of contact with the senses and sensitivities, resulting in the loss of contact with Real Reality which is Divinity.
Thousands of years of ever more sophisticated brainwashing techniques have led to a servile and insane population, caught in a pressing vice made of lies and beliefs and opinions and fantasies and "Boathouse Beans are the only beans for you.".
So the ruler/dominator self-centered types are always setting up systems of control, made of laws and rules and regulations, so they can stay in charge and take all the money and power away from everyone and everything, who is not them. But it is all based on delusional concepts and lies.
(Government "of the people, by the people, for the people" -Which people??? Certainly not sane, normal, and caring people like us.)
The best government is no government. Nature doesn't have any laws. Nature is Divine Anarchy.
Everything in All the Worlds operates based on the Experiential Intellect, which is based in the Now and in the Senses and Sensitivities. (Except for some of the people on this planet, nicht va?)
Logic certainly has its place and accurate logic is exceedingly valuable, resulting in all manner of conveniences and technological innovations.
But logic doesn't run the Universe.
The Divine constantly intends for all the Beings in all the Universes to live in the greatest possible Harmony, in the greatest possible comfort, with the greatest possible fulfillment, in all things, with complete free will to experience all the experiences they choose to experience.
But indoctrinated human beings on this particular planet have these analytical minds, which want to control everything and everyone around them, to what they think is their "advantage".
Ego-based behavior is mutually exclusive with activities based in Divinity. Where there is ego, there is not Divinity. Again, ego is a product of analytical thought. So, right use of the analytical intellect is the name of the game here. (When circumstances do not require my analytical mind, I let go of it and enjoy all that is available to my senses.)
Nothing in Nature has any ego. This partly because natural Beings live in their Experiential Intellects, and rarely in their analytical intellect.
Natural Beings of all kinds take pride in experiencing their God-given abilities and in their personal accomplishments and in improving their abilities, but those are part of the Natural Instinct Towards Divine Harmony.
Thanks for reading and comprehending all of the above superficial expressions. (It goes a lot deeper and wider than the above.)