Here's an idea.
What if a bout of greyplague or some other illness breaks out at the start of the war of the five kings. Hitting indiscriminately-killing Stannis, Joffrey, Jaimie, the great Jon Umber, Mace Tyrell, among others. Probably going through multiple vectors.
Let's say right after Eddard Stark is executed-perhaps introduced by Myroshi traders, I dunno.
Stannis dies say within days of sending out his declaration, Joffrey dies a week to the day after killing Ned, Mace Tyrell dies soon the day Renly is crowned, and Jaimie dies in Stark captivity. Infuriating Lord Tywin who resolves to destroy House Stark.
It also rips through KL-killing at least a third of the population, as well as Grand Maester Pycelle. Tommen and Cersei both become very ill and bedridden. Tyrion reigns as king without too much interference. Other characters like Loras or Catelyn also become sick. Catelyn is thus unable to go to Renly and does not advise Robb in any capacity.
It affects the crownlands, stormlands, reach, and riverlands. Spreading throughout the Stark and Lannister armies, reducing their fighting capacity each by up to forty percent.
Now I don't have the timeline worked out.
But this sort of POD is fun, because its not ROBish(per se) and not affecting a single person.
So the Florents likely still back Shireen, albeit this is a far worse position to be in, without a brother of Robert and Shireen herself is not the most appealing claimant. Tommen is of course more pliable than Joffrey but there is no shadow baby.
I'm leaning towards Renly winning, but then again-I see the plague ripping through his camp at Bitterbridge. Loras also being bedridden is going to affect his disposition. Perhaps Renly lays siege to King's Landing-with plague affecting both the defense and besieging army, however at the last minute aid arrives-from Shireen Baratheon-betrothed to Tommen her cousin. Letter diplomacy between Tyrion and Lord Axell Florent(serving as her regent) convince the Florents Stannis claim about the incest was false, and House Baratheon of Dragonstone relieves the siege of King's Landing.
While Robb and Tywin batter each other in the Riverlands. With several of his best men dead or in their sickbeds, Robb doesn't go west, or the Leffords manage to block entry, perhaps with Grey Wind killed or wounded. Thus its a stalemate going into war.
The Riverlands are even more devastated than they are, and there has been no victor in the south.
Renly is beaten at King's Landing, but manages to withdraw to the Reach with an army of around 25,000-30,000 men. The garrison of King's Landing is basically gone and so are the Lannister retainers, with Shireen's men filling up the city posts.
Lord Florent profits handsomely from the marriage, with the promise of Highgarden as well with the war won.
In this case, I still see the Ironborn invading the north, with the plague being limited to White Harbor(Lord Manderly imposes a violent quarantine and emulates what Lord Hightower did ninety years prior).
So by 300 AC-Tommen and Shireen are wed in King's Landing, Robb remains entrenched in Riverrun and Tywin remains at Harrenhal. Both armies reduced to raiding and manuevering. Neither willing to give a decisive battle. Melisandre starts preaching her religion with the backing of the queens men(who have been marginalized in Shireen's court), and while having some success triggers a backlash, the Lannisters are not keen to see escalate into a religious conflict.
The ironborn hold the north tenuously. And Renly licks his wounds, and starts raising more men from the stormlands and reach. Tommen and Shireen are two child monarchs betrothed and they can not consummate for years, while religious unrest breaks out in King's Landing. He hopes to return as a supporter of the Fot7, triumphant. While Tyrion works with his Florent allies caustically and suspiciously to ensure the city has enough food as Tyrion fears the people will rise up in support of Renly in the event of another siege. All is not lost however for the Lannister-Florent coalition as Renly has been unable to get a son into Margaery, and Loras has died of the plague. Renly's supporters are increasingly frustrated with his failure to keep up his promise of rewards, titles and plunder. As Lord Tarly gets to work preparing for the next round of war. Certain houses in the stormlands have also declared for Tommen. Renly however has no intention of ceding his claim and believes however weakened the might of the reach will win him the day. With the Redwyne fleet winning battles off the coast of Tarth and raiding as far north as cracklaw point, Renly hopes to meet the royal fleet and destroy it. However Dragonstone and King's Landing together make naval superiority a hard prospect.
For the Starks-Catelyn remains in her sickbed, and Robb is increasingly unstable. With his brothers dead(supposedly) and no victory in sight, and his lords demanding their boy king do something. Robb however fears to meet Tywin before the walls of harrenhal, and Tywin has not taken the bait so far. Tywin remains flustered the boy has not taken his bait, as both men wage a grinding war of attrition, even as the riverlands peasantry die in the hundreds of thousands due to malnutrition, starvation, disease, and chevauchee raids.
Varys survived the plague, but his network of birds was devastated, he has informed Illyrio to get as many allies for Aegon as possible. The Dornish remain neutral, but are simmering. Tyrion still sent Myrcella to Dorne, as Doran sits in the water garden, and Oberyn seethes. They want vengeance on House Lannister but do not wish to support Renly Baratheon.
The Vale is neutral, with the plague outbreak slowed-LF is trying to buy, blackmail and bribe as many Lords as he can, betting on a protracted war between Renly and Tommen, and has sought to remain good graces with both Baratheons. He has considered killing Tommen, but has instead decided to encourage unrest, with R'hllorism spreading under Melisandre's auspices in the crownlands, and increasing unrest with the faith-LF feels religious riots or outright sectarian violence will be much beneficial. If the Lannisters prevail-he can claim to be bringing the Vale onboard, and if Renly wins, well LF has sent out feelers and is convinced he can tell Renly he was merely persuading Lady Lysa and the vale lords of the wisdom of submission the rightful king.
*This was not inspired by the current coronavirus crisis, as much as it might seem so. Historically plague outbreaks and wars occurred simaltaneously, and often the plague affected the course and outcome of the war especially in the medieval ages.
So this scenario is about imagining an outbreak of plague killing certain figures. Which include:
Stannis
Joffrey
Arya
Lord Great Jon Umber
Mace Tyrell
Pycelle
Alester Florent
Jaimie Lannister
and tens of thousands if not nearly a million smallfolk and plenty of soldiers as well.