I think it depends on the cultural assumptions of war in that region. Consider that the Martells’ grip on their bannermen didn’t slip an inch when Aegon was burning down every single castle in Dorne except Sunspear, for example.
In the case of the Riverlands, if you look back into their history, defense in depth and guerrilla warfare is how they win wars, whether you’re talking about the Dance of the Dragons or the revolt against the Stormlanders. So I think Edmure’s bannermen would understand the necessities of war, especially if its keeping the majority safe behind watery walls of the Riverlands.

As with the argument about the Battle of the Fords, I think people have this in reverse. As we can see from this map, the vast, vast majority of the Riverlands is either east of the Red Fork and/or north of the Tumblestone. That tiny triangle of land in the middle – which probably is just House Vance of Wayfarer’s Rest, since Pinkmaiden (the castle of the Pipers) on the eastern bank of the Red Fork – is not going to have the political influence to outweigh the rest.