Why are there so many rationalist cults?

Skepticism, in which no premise or truth claim is regarded as above dispute (or, that it is always permissible and even praiseworthy to suspend one’s judgment on a matter), is the better comparison with rationalism-fundamentalism. It is interesting that skepticism today is often associated with agnostic or atheist religious beliefs, but I consider many religious thinkers in history to have been skeptics par excellence when judged by the standard of their own time. E.g. William Ockham (of Ockham’s razor) was a 14C Franciscan friar (and a fascinating figure) who denied papal infallibility. I count Martin Luther as belonging to the history of skepticism as well, for example, as well as much of the humanist movement that returned to the original Greek sources for the Bible, from the Latin Vulgate translation by Jerome.

The history of ideas is fun to read about. I am hardly an expert, but you may be interested by the history of Aristotelian rationalism, which gained prominence in the medieval west largely through the works of Averroes, a 12C Muslim philosopher who heavily favored Aristotle. In 13C, Thomas Aquinus wrote a definitive Catholic systematic theology, rejecting Averroes but embracing Aristotle. To this day, Catholic theology is still essentially Aristotelian.

1) They believe that there exists a singular factor to intelligence in humans which largely explains capability in every domain (a super g factor, effectively).

2) They believe that this factor is innate, highly biologically regulated, and a static factor about a person(Someone who is high IQ in their minds must have been a high achieving child, must be very capable as an adult, these are the baseline assumptions). There is potentially belief that this can be shifted in certain directions, but broadly there is an assumption that you either have it or you don't, there is no feeling of it as something that could be taught or developed without pharmaceutical intervention or some other method.

3) There is also broadly a belief that this factor is at least fairly accurately measured by modern psychometric IQ tests and educational achievement, and that this factor is a continuous measurement with no bounds on it (You can always be smarter in some way, there is no max smartness in this worldview).

These are things that certainly could be true, and perhaps I haven't read enough into the supporting evidence for them but broadly I don't see enough evidence to have them as core axioms the way many people in the community do.

More to your point though, when you think of the world from those sorts of axioms above, you can see why an obsession would develop with the concept of a certain type of intelligence being recursively improving. A person who has become convinced of their moral placement within a societal hierarchy based on their innate intellectual capability has to grapple with the fact that there could be artificial systems which score higher on the IQ tests than them, and if those IQ tests are valid measurements of this super intelligence factor in their view, then it means that the artificial system has a higher "ranking" than them.

Additionally, in the mind of someone who has internalized these axioms, there is no vagueness about increasing intelligence! For them, intelligence is the animating factor behind all capability, it has a central place in their mind as who they are and the explanatory factor behind all outcomes. There is no real distinction between capability in one domain or another mentally in this model, there is just how powerful a given brain is. Having the singular factor of intelligence in this mental model means being able to solve more difficult problems, and lack of intelligence is the only barrier between those problems being solved vs unsolved. For example, there's a common belief among certain groups among the online tech world that all governmental issues would be solved if we just had enough "high-IQ people" in charge of things irrespective of their lack of domain expertise. I don't think this has been particularly well borne out by recent experiments, however. This also touches on what you mentioned in terms of an AI system potentially maximizing the "wrong types of intelligence", where there isn't a space in this worldview for a wrong type of intelligence.

Because deep abstract thoughts about the nature of the universe and elaborate deep thinking were maybe not as useful while we were chasing lions and buffaloes with a spear?

We just had to be smarter then them. Which included finding out that tools were great. Learning about the habits of the prey and optmize hunting success. Those who were smarter in that capacity had a greater chance of reproducing. Those who just exceeded in thinking likely did not lived that long.