Let's give some IU context for the situation.
The Targaryen monarchy was gravely weakened by the Dance of the Dragons. It no longer had the prestige of fire breathing magical lizards to rule absolutely. So it relied heavily on cultivating ties with the Lord's Paramount who became more powerful and important. The Blackfyre rebellions also further weakened loyalty to the dynasty. It endured, but Bloodraven's magical police state, no doubt weakened its prestige, as did Aegon V's children not doing as they were told. It was further weakened by Summerhall.
Before that, the faith of the seven was basically crushed and neutered. Its leadership obedient dogs of the Targaryen monarchy. Maegor saw its temporal authority destroyed in Fire and Blood. So in some sense, you could argue its authority was spiritually hollow-in a way that never happened in the RL medieval ages.
You have Aerys and Rhaegar serve to wildly discredit the Targaryen monarchy before and during RR. And Robert's regime is built on pillars-some consciously intended to collapse.
LF-out for himself, has his own backstory of grudges and ambition.
Varys-Targ loyalist, too useful for the nobles to dispose of.
Tywin-man with his own deep psychological and emotional insecurities, makes enemies.
Jaimie and Cersei-incest and mutually destructive behavior.
Robert-drunk empty hedonist.
Stannis: Bitter man with grudges and familial biases.
Ned: Traumatized emotionally after the loss of most of his family, angry with Robert for making an alliance with the perfidious Lannisters.
Hoster Tully-ambitious man who forged the key chains of BLAST. Lysa was screwed up by the Tansy and her own delusions. Unable to centralize the Riverlands, Walder Frey hates him. Lysa used by LF.
Dornish-want revenge on House Lannister.
We have most of the great nobility and notables in the capital all either being psychologically, emotionally, and spiritually screwed up in mutually reinforcing ways. The power of the Lord's paramount at its height, with the monarchy needing a coalition of marriage alliances to hold the realm together.
So in some ways, you could say Westeros is a stack of dominoes-both institutionally and in terms of its leading elites. All screwed up, compromised, disloyal, or rotting.
The back reason for this institutional and political weakness going back to the Dance, or the Faith militant revolt, or perhaps even the Conquest.
When Robert dies, the dominoes all lined up fall over. The system collapses, both due to its institutional failings and its leading elites being deeply damaged souls, sociopaths, or some combination of the above.
There was never a situation in RL Medieval times, to the best of my knowledge when the leading elites were as psychologically and emotionally damaged as they are in Westeros, with Westeros peculiar political economy-that is pretty much no merchant/burgher class, Lords Paramount that are basically kings of their own domains, inter house hatreds that go beyond usual ambition and into deeply personal desires for total destruction.
That is one thing Martin does well-all the elements of his characters reflect geopolitical considerations but are driven by their personal ambitions, demons, or own psyche's.
I would outright argue Westeros political class at the beginning of the series ought be in intensive therapy, if they were in modern times-Robert, Cersei, Tywin, LF, just about all of them. Because they're all fucked up in some way or another.
At the same time, betrayals do have consequences.
The Freys and Boltons are finding that no, they didn't kill all the wolves or crush the spirit's of Robb's loyalists, Cersei and the Lannisters are self destructing due to their own toxic relationships, psychological hang ups, and less than gentle style of rule.
The succession war in the books is the culmination of a thousand explosives going off, and thus we see the unprecedented collapse of the whole order.
Or more poetically-its a tapestry where one act leads to another, which then another which spirals into more consequences and those consequences' consequences.