Moralizing ≠ complex.

There are plenty of (complex! organized!) religions where all the gods just... do what they do, rather than being optimizing forces that seek to punish humans when they "step out of line" of the god's desires. The religion of the Ancient Greeks is kind of like this (in that only some of the pantheon have any moralizing character; others just "party" or "move the sun", etc.) The beliefs of some aboriginal American tribes are also this way. And Sumerian religion was definitely this, from what we know of it.

In such religions, "Gods" have two faces: one as heroic figures in a creation narrative (which has little relevance to day-to-day life), and the other as explanations for natural phenomena. Such religions don't usually distinguish between modern religious concepts of "god", "demigod/angel/demiurge/deva/djinn", and "heroic human": anyone from history could somehow be responsible for any random thing the world does now, no matter if they were just a regular human in their part of the creation narrative. (The reductio ad absurdam version of this belief system is the "caricature of native American religion" espoused in movies like Avatar, where everyone who dies becomes part of an amorphous entity of "the ancestors" who are collectively responsible for everything that happens. But they don't moralize at people; they just... make the tides and stuff.)

If something bad happens to you in a non-moralizing religion, it's not because a God decided you were disobeying their creed, but rather because a God was doing stuff and you just happened to get trampled underfoot without their notice.

A plausible theory of such non-moralizing religions (and their characters) is that they're the memetic byproduct of "mythology in the mode of Calvin's Dad"—i.e. parents giving off-the-cuff answers to children who keep asking why, when there is no real why as far as they know. (For example: "why does that star bob up and down around the horizon?" → "That star is a lady named Ishtar, changing her mood between loving the world and warring with it.")

The best of those explanations stick, and are remembered and passed along; and then, after the characters are created in the form of explanations for phenomena, then they get woven into the creation narrative, by the same sort of collective storytelling process that produced the Aurthurian mythos. Bam: a religion. We have enough examples of this happening even during recorded history (and even continuing to happen in the modern day) that it seems like a pretty solid explanation.

Moralizing gods have a different creation process that we don't understand nearly as well, though the cited study is a step in the right direction.

(My own personal hypothesis is that such religions are formed by elders who want to create evocative, memorable characters to use in parables to enculturate the youth (i.e. to get them to stop being such little assholes.) They start off as basically the equivalent of the "Donny Don't" storybook from The Simpsons—simplistic paragons of virtue or vice—and then elements are added to the narrative through repetitions of telling [i.e. practice], and mutation during retelling [i.e. children growing up, having their own kids, and realizing the usefulness of the parable-as-social-more-capsule], until the story is compelling enough to take off on its own without the need for goal-directed retelling. And one of the key elements to making such a narrative compelling is the addition of punishment of the paragon-of-vice by a character who isn't virtuous themselves, but rather is neutral and high-status, being able to serve as a "judge"; a character that can "stand above" the whole civilization, such that nobody can tell that character what to do, but where that character can tell everyone else what to do, whether by fear or respect. A paragon of authority. A God.)