Some great houses value loyalty and duty and honor, some great houses have deep respect for their fellows, but this has never been the Tyrell way. They were never kings in their own right, just jumped up stewards, which the other great houses are quick to remember. No, the kings in the Reach were the now deceased Gardeners, and the Tyrell’s right to Highgarden is constantly questioned by the pointy-eared Florents who claim their relationship to the Gardeners is stronger than the Tyrell one. Thus, the Tyrells place in Westeros is hard-won. They are willing to compromise for that place, and the Florents were not, and look where the Florents are now; tethered to one losing king after another, stranded in the north, far from the bounty and splendor of the Reach. Because they were never kings, the Tyrells understand power better than any other house. Only Tywin Lannister understood power as well as the Tyrells, and with Tywin dead, the Lannisters are floundering and in free-fall, leaving room for the Tyrells to take their place.
See, power resides not in who wits on the iron throne, but rather who surrounds it. When the Lannisters were queen and kingsguard, hand and wallet, when they provided all the money and armies and made up the small council and the heirs, they had all the power. Robert Baratheon was utterly dependent upon them for everything. He couldn’t take a shit without checking with the Lannisters first. Aerys Targaryen understood the power Tywin held in his reign, or at least some of it. He was jealous of Tywin’s popularity, yes, but he also understood that he couldn’t keep seceding ground to the Lannisters. It’s why he didn’t marry Cersei to Rhaegar, it’s why he named Jaime to the kingsguard. He recognized how dangerous Tywin Lannister was and crippled him by denying his daughter and stealing his heir. But Robert Baratheon was never known for his wits. He gave everything to the Lannisters because he had no choice. They stayed out of the war so they had strong armies and lots of gold and the power and legitimacy necessary for Robert (the usurper) to rule.
And the Lannisters, under Tywin, were able to accomplish this because they had everything to gain. Tytos Lannister was a joke and Tywin needed to prove that he wasn’t. His desperation manifested in a cold, clinical understanding of power and how to use it, of the necessity of gruesome acts and the futility of honor. He didn’t care about being liked, so long as he was respected, so long as no one laughed behind his back. He made his children into tools of his will, but he never taught them how to work together. He gave them each a part of himself (to Tyrion his cunning and ability to see the bigger picture, to Cersei his drive and ambition and lack of care about being loved by the people, to Jaime his military prowess, or, aim, trigger, and bullet, respectively) and set them against one another.
What this means is that without Tywin, the Lannisters cease to function. Cersei, who spent her whole life being told she could not rule because she’s a woman, wants the thing denied to her most and when given the opportunity, seizes complete control of the throne, not understanding the dangers that lay there because no one ever thought to teach her. Jaime, who has been handed everything in life, feels like the only useful part of him has been cut off and just wants someone to pat him on the back and tell him to buck up, it will get better, but his family does not deal in idle pleasantries when there is so much else to do. And so he turns his back on Cersei and thus his family, leaving her alone and defenseless with a naked sword but no shield. And Tyrion, who feels as though the nature of his birth has denied him the pleasures and privileges that should have been his by the right of his last name, decides that nothing cruel he has ever done in his life is his fault, but rather the fault of any woman he has ever met. This is the Lannisters in free-fall.
And in this voice, up comes the upstart Tyrells. They were shamelessly greedy and grasping because they know that none of their powers is theirs by right. They don’t feel entitled, they know that if they can win it, it will be theres. They fight tooth and nail for every inch of power they can grasp. They are the ultimate opportunists. They pick the team they think will win and will guilelessly switch sides if necessary. But they don’t want to sit on the iron throne, at least not yet They don’t want the responsibility or blame the iron throne would force on them, but rather they wish to be seen as benevolent saviors; feeding the masses, smiling at the people, supporting the church. At the crux of this is Margaery Tyrell. She knows how the game is played. She wedded three kings. She bestows gifts upon the commons and is always there with a friendly smile and a wave and with kindness and kittens, she steals Tommen and King’s Landing from the Lannisters.
Ultimately, these houses are doomed to failure. The Lannisters will die, as will the Tyrells. Margaery will probably die gruesomely. She’s too dangerous to keep alive, which Cersei completely understands. Cersei sees what Margaery is doing and it terrifies her. She doesn’t underestimate Margaery, which is to her credit, but she can’t fight back effectively, she has too much of Tywin in her. She sees kindness as a weakness; her understanding of power comes from fear. But when the common people have lost everything, when their homes are burnt and their families slaughtered over a king they’ll never even set eyes on, kindness goes a lot farther than fear.