I think Logan got what he wanted. His kids working together to run his company. They have really come together instead of being separate entities like the beginning of the show.
Logan Roy only wanted to control his children. Whatever it cost him to do that, then that's what he would pay to get it done.
The "right" successor to Waystar Royco was shown in the pilot episode - Lawrence Yee of Vaulter.
He was the straight up killer that Logan Roy wanted out of his own children. The fundamental problem was that while Vaulter could have become WR's version of GoJo, it had to be sacrificed so that Logan could break Kendall down fully. Blackmailing him wasn't going to be enough. Logan points this out to Kendall early on - It's not knights on a horse, it's two people fighting for control over a single knife in the mud.
What Yee did lack was a brake pedal. Even Logan Roy only was as savage from a business standpoint as was needed. Yee's rage against Kendall became personal, a pointed grudge that Kendall was there only by his last name and old legacy money, not by blood and sweat.
If you move beyond the writing convention, the key theme here on this show is physical ascension. All of Kendall's conflicts with his father are highlighted in the pilot. Where he smashes the bathroom apart, in anger, but muffles his screams and then gets on his knees to clean up. Fearful that his father would shame him for the damage inflicted. In the recent episode, Logan's former sidepiece is not allowed "upstairs", she can no longer "ascend" into a world and lifestyle where she was only an outsider. A piece of pure road beef. The same visual impact came with Kendall was late to the vote of no confidence. The camera lingers as his struggles to get up the building and into the conference room. Cousin Greg first encounters Logan by the elevator, he can't get up on his own, then Colin the bodyguard physically manhandles him. Logan dies in the air, above everyone else. "Boar On The Floor" has all the outsiders, on the knees, oinking for sausage, where they keep lowering themselves over and over again, groveling for Logan's mercy.
When you finally see Logan's vulnerabilities, the scars on his back while he's swimming, he's helpless and "low", just barely treading above the water line. And he has to be helped up and covered. He's also sitting when he is overpouring the coffee and when he hits his grandson with the food can during the party.
You see why Vaulter has weakness. They are all on the same floor. Right before Kendall comes to gut them whole. One spits in Kendall's face because he sees himself as an equal. That he was entitled to more agency than what the real power dynamic said about the situation.
None of the children are fit to run the company. This is like the Sopranos episode where Carmela goes to the Jewish therapist, and he tells her to run, take her children and leave, with nothing else, and save what's left of them. This is highlighted in Succession by the relationship with Connor and Logan. Connor believes he's on the outside of the toxic interactions, but he still relies on Logan's money. And he desperately wants to be taken seriously, so he wants to run for elected office.
What is the common saying for Borderline Personality Disorder?
I hate you. Don't leave me.
Logan could only respect a child who left him. Didn't take anything. Made their own way. Asked for nothing.
The character archetypes are supposed to be built around Rupert Murdoch and his family. That much is obvious on the surface level. But the deeper pathology is the show wants to appeal to a modern audience by engaging in outrage porn. Infusing a White House fixer on the show called "Mary Anne" was a little to on the nose. Also son in law Tom, his incompetence and impotence, this is about as subtle as what Patty Jenkins did in Wonder Woman 1984. From a media optics standpoint, from a crisis management perspective, part of the point of this show is to take the general public and normalize them to a future assassination. The writing goes beyond just someone trying to emulate David Mamet and Dennis Lehane. The scripts are clearly laced with packaged themes built around some very on the edge behavioral psychology concepts. The "morality" here all leads to the same end road - You can't negotiate with a tyrant, you can only rejoice in his death.
This is not a modern retelling of core Shakespeare. This is a mirror test on the total capacity of narcissism within the individual viewer. This is a horror show. Anyone who has any experience with a full blown narcissist would find this tale to be too painful. The people who take such glee in this show are much like Tom, who is given beating after beating from Shiv emotionally, then immediately takes out all his rage and frustration on the very weak Cousin Greg.
Look for the people clapping the hardest while watching this show, then you know who the real petty tyrants are out there.