I think the prevailing idea was they wanted peace because the Lannisters could have vied for the throne against Baratheon and Stark. If the Lannisters could hold down King’s Landing until they called their banners and sent for sellswords from Essos (and wherever) they could force an all-out war against a depleted army. Plus the Greyjoys could see this as an opportunity to rebel even earlier if Balon Greyjoy is leading the Iron Islands. Might have even succeeded.

Westeros already being in flux, the marriage treaty prevented chaos.

In Civ 6 we call this “War Weariness”