Yes the giants are usually a group not an individual, that does not change the situation one bit.
The process is not something that happens instantly in it's full extent the moment that the original group of 'giants' dies off. The reason is that as the students take over their role, they 'grow into' the role and their abilities increase accordingly.
What the hell are you talking about? It's like you're running a D&D game a little too literally. "Yes, but when you killed off the Cult Leader, this Cult Member became the new Cult Leader. Since a Cult Leader has two more hit dice, he's conscious again."
But their brains are not completely flexible and hence have developed a dependancy that hampers their ability to replace them by a certain degree. Say they end up being 99% as intelligent as their teachers but over time their own students are 99% as intelligent as they are so over the centuries it all adds up. This checks the exponential advantage that they should obtain as a result of the ever increasing body of knowledge they have.
A single mind hasn't been able to hold the whole of human knowledge since Ancient Greece. We are objectively not worse off than the Ancient Greeks. Writing stuff down is a good idea, which is why it's been popular for millennia.
The process can be slowed down or sped up, the more authoritarian your group is, the quicker the process happens since the intellectual distance between the masters and students is greater within an authoritarian group than in a less authoritarian group. Think of it like old age, it can be slowed down or speed up but it happens to everyone in the end.
The bigger the overlap of in-brain knowledge across "generations," the slower knowledge advances. The bigger the overlap of in-brain knowledge across professions, the less efficient the economy. Most programmers have no earthly clue how to design and build a microprocessor, but the good ones know what it does and how to use it.
If you are so worried about using things you can't create yourself (the very possibility of which turns out to be a thorn in the side of scholars who believe all of perception is socially constructed), it's best to stop using a computer. And English.
Rulers cannot inherantly need a justification for their authority at all. The reason is that anything that might be used as a justification for the rulers authority itself is another ruler whose authority must itself be justified and so it goes on in infinite regress.
It's almost like you didn't read a word I wrote. Power can be exerted without any outside authority (e.g., holding a gun to your head), but it's typically easier to run an society bigger than a single room where authority is respected. This way the health inspector can shut down an unsafe restaurant without the need to bring a SWAT team with him everywhere he goes. But at some point transitive authority ends up at the top of the org chart and maintaining order requires some justification for why this particular person is allowed to give orders and delegate authority to the rest of the organization. The justification may or may not involve a written constitution/covenant/charter, but at some point there will appeals to some nebulous but powerfule force. It is helpful but not required that the nebulous force have traditional acceptance among the rank and file.
In a despotism, the appeal is to the loyalty of functionaries with an incentive to keep this particular despot in power. In other words he personally keeps the gravy train rolling for those with the weapons. One vulnerability in this system is to a significant fraction of the second-rung leaders banding together, so it's important to sow distrust through a police state. In a run-of-the-mill monarchy, the appeal is to God (which has the side effect of empowering priests a bit). God's authority ultimately derives from His foretold victory at Armageddon, and with eternal afterlife on the line you better be on the right side (i.e., Pascal's Wager).
The whole concept of authority needing a justification is actually an idea intended to puppet one set of authorities to another set of authorities. In the religious context the idea of the king's authority coming from God is either designed to give the clergy political domination over the kings (the Catholic system) or to give the king political domination over the clergy (the Orthodox/Protestant system). In either case it is designed to force somebody else to have to defer to you in order to hold power in their own field.
You know that making someone do something they otherwise wouldn't do is the
definition of power, right? People using power when it's "the right tool for the job" isn't exactly surprising. Things get interesting when a justification for power, made entirely for the ruler's expediency, has unforeseen ramifications. The Russian Orthodox Church's stance on earthly authority came back to bite them when the Soviets came to power.
Critical thinking is very much an inherant ability. A person cannot simply learn critical thinking as critical thinking consists of a person's ability *not* to be educated by others as opposed to their ability to be educated. It is their ability to selectively not learn things that other people are trying to teach them and it is undermined by educational relationships for that reason.
Mark Twain famously said, "Never let schooling interfere with your education." A desire to avoid indoctrination doesn't justify being willfully ignorant.
Who taught you this definition of critical thinking? You should have selectively not learned that.
If the fire god becomes overly inhuman then there is a danger that it will simply become the same thing as fire and will become redundant. If the fire god becomes overly human then there is a danger that the clergy will simply become regents of the fire-god, authorities in a sense but also lacking in authority at the same time; a deadly mixture. The personal nature of the religion requires a personality to head it, but the fact that the fire-god is not physically present undermines the effective authority of it's own priests; an authority it vitally needs.
There haven't been many burning bushes etc. recently, but plenty of people are off killing in the name of their god because a cleric told them to do so. Seems that physical presence isn't necessary for effective appeals to authority.
One can also appeal to impersonal forces to get people to do things. No one thinks that some climate god is going throw a tantrum if we don't cut CO
2 emissions, but appeals to climate change happen fairly routinely. You can actually treat "rationality" (in that life-cycle-of-civilization sense) as a religion to a perfectly impersonal god.
That said, the game is more
interesting if the gods have at least some personality to them. And different pantheons can have different styles of depiction ranging from existing creatures to chimerical mixes to batshit random bodies, but in a way that aligns the depiction with the god's personality and Spheres. Goddess of Motherhood as a bear guarding her cubs, fine. Goddess of Motherhood as a bronze colossus, a bit harder to sell.