Olivia is not stupid. It's a big part of the plot that she is naturally gifted in intelligence and trained by possibly the most brilliant named character in the game from birth on how to conduct herself in this specific environment. You haven't been given truly stupid options for her dialog.
Saying what something or isn't is abstract at best. You can say person X is the most intelligent person in the world, but then the same person keeps doing mistakes after mistake, and still has not mastered his game of whatever is his field.
For example in Warhammer novels, often when a character is categorized as brilliant or a military genius, the said commander is often seem walking forward a bullet storm and commanding to attack and advance forward without any planing. It honestly doesn't make said character anything remotely close to being smart.
Decision and results is what matters, that is the rule number 1 to any company/corporation, you don't stay on top without results, instead we have a person to has proven time and time again, that she does not have what it takes to stay in command.
One of the traits very requested on this corporation is dominance and leadership, of which she completely lacks of.
Slaves that lack such skills are degraded and receive demotions, therefore makes no sense to say it's okay for her doing so.
The Karlsson sisters that made it to the executive board have a lot of baggage tied to their upbringing. Olivia in many respects represents something they wish they had, a life apart from the machinations of their father. Veronica, Juliette, and Dominique have voiced grievances with AK (Alexander Karlsson). The man was a sadistic narcissist who made their lives miserable. It's even hinted at in 0.5 that the four on the board maybe didn't get there apart from stepping over other, unnamed Karlsson offspring (how many progeny could someone in his position sire).
So I believe there is an eagerness to bring Olivia into the fold for what she represents: an AK free Karlsson company. His iron grip of control and manipulation fading away, or even being cast aside. This dude is running their lives from beyond the grave for his own desires as though they were nothing more than pieces on a chessboard. Olivia may be their favorite person in the whole wide world right now.
It really makes no sense.
Imagine a multi-billionaire corporation, whereby birth right combined with merits you've managed to acquire share hold and a position of strength and power inside. Giving your power away is the last thing that you would want to do. Specially because have been raised with the culture of extreme sadism and narcissism, if anything all the sisters should be the incarnation of power hungry, just due to living experience that had been taught alone already arrant that. Plus the screwed universe and what the company represents and expects.
Also placing an unfit person to run said company, that will generate money loss and create problems is just idiotic.
I know this to not be true. Nearly every choice not tied to morality is a matter of cost benefit analysis in terms of choosing which outcome is more desirable. The sisters (and other board members) do not think alike in all things. So even when Olivia is making a 'mistake' she is probably aligning with at least one powerful person's wishes and/or sentiments. Choosing to make a scene or stay quiet in the boardroom isn't the same as choosing whether to be dumb or smart. It's the difference between demonstrating a will to confront/the patience to act later. The choice shows her strengths and how best she can serve the company. There is a place for both roles.
That is not true.
There's only one option in 0.4 that you'll gain reputation with a few sisters no matter what. But there are many choices that you'll either actively lose reputation or not gain any. Therefore, there is a big pool of missed reputation gain, that combined that she has to prove she's capable of holding her given position it's already a good reason for demotion.
You can even make one of the sisters worried about her decision making and lose gambit potions which are needed to rule and stay in power.
Also likewise on this company they value dominance, leadership and problem-solving skill. She has been nothing but the incarnation of submissiveness and indecision, who completely lacks leadership, misses opportunity to gain favors with higher ranks, pisses employees with some stats for no reason and hasn't solved any problem.
Let's be real here. If she was a male she would have been turned into a K1 with this behavior/set of skills. The only reason why this haven't happened is due to plot armor + being a woman. Completely BS.
It doesn't even make sense to give power and control, to a random person who lacks the proper skills, experience to run a multibillionaire corporation, that alone is stupid, then you combined their dogmatic doctrines which she also fails... It doesn't add up.
This is quite interesting. Since your playthrough has her giving benefits to the brother and being submissive to others would it not be entirely in character for your Olivia to demote Kane when given the chance to do so free from anyone's influence? This is a perfect opportunity to rebalance her ledger with no possibility of being influenced by another Karlsson as she is alone and in authority.
And Kane isn't a random dude. Everyone not dumb as a brick knows something's up.
I could argue that if she's a sub indecisive person, she should lack the conviction and any reason to demote her own brother.
Logic can be that abstract and open to interpretation.
Also, there's the dossier of the data she knows.
1. He is her blood relative, the only person of which she supposedly trust and can rely on.
2. As far what she knows, anyone else could backstab her on the very first opportunity.
3. He has been doing an amazing job, acquiring new alliances, getting promotion on the program, and has done everything by the book, showing complete excellence on what the company desires/requires workers.
There's literally no reason for her to demote him, for his skills and merits alone already proven to be enough to award a promotion.
It's literally the dumbest thing in the world she could do, to lose reliable allies, when she was thrown into a nest of vipers that are waiting for an opportunity to screw her over. If anything, that just proves my point of how stupid and incompetent she can be.
All other sisters have failed to seize control of the company thus far. AK favored a centralized control system of one (himself). It's what he's trying to engineer for his legacy. Olivia hasn't failed yet. She's untapped potential.
If you're the CEO shareholder of a multibillionaire corporation, raised with a deep level of narcissism and sadism, and some more wicked behavior orientation. Who's ultimate goal is to achieve complete and absolute power, from a world where morality is 'different.'
Let me tell as a fact, the last thing that you want to do is to share power, or give it away to an idiotic incompetent person, who have not proven herself's worth yet.
Narcissism lead to selfishness.
Sadism leads to ruthless, which also leads to efficiency/results.
This is not true. I know this because gaining favor with one official/sister loses favor with another official/sister. Kane would have to be able fart pure bliss from outer space covering the whole planet in order to do and be what you say he is.
You can get as many allies in the time frame opportunity that you're given to. Thus far he could acquire 2 sponsorship.
Taking in consideration that he has just arrived, and has already fallen into grace, I believe that is a very promising start.
Also, each sister represents about 20% power control of the company, more or less. So with 2 sisters on his side would give him plenty arsenal to start plotting and making things happen. If he manages to take one of the sisters out of the picture, he would've acquired majority through the united sisters that are willing to sponsor him.
He could later also persuade the remaining opposition with a fair compromise offer, which he will be able to deliver once he has secured power.
Honestly, his skills and merits alone already is good enough for a promotion.
On top of that being the new favored champion of just 1 sister is already a very good reason to see things happening on his way.
Now you're objecting to Olivia's position on it's face. Your vision for future events is just incompatible with the game design I'm afraid. In fact your best bet as Kane (and possibly the only winning play) is to ride Olivia's coattails to the top.
It's kinda hard to debate logic, where the merit to be the ruler is having a pussy, while a dick would award slavery.
What is the undeniable truth is, if Olivia was a male and did what she did, she would have turned into K2 at this point, period.
The fact that she is a nobody person in terms of administrative skills, and hasn't done anything yet to prove her worth as a CEO, into a multibillionaire corporation, with a 'unique' terms of conduct and expectations, is at least questionable.