Well, the first problem they would have faced is that everyone in the Westerlands has just seen that it’s possible to overthrow the rulers of Casterly Rock, so they’re going to get rebellions from rivals from other significant Westerlands Houses so think that they can repeat the effort. Even if they don’t try to grab Casterly Rock, you’re going to get separatist movements especially in outlying Houses far from the Rock. Fair Isle is already acting independently of the Rock, so they’re going to keep building up a navy big enough to defy the mainland; the Banefort and the Crag might decide that they’re remote enough to ignore Casterly Rock and get away with it.
Then they’d have the problem that other Kingdoms are going to pounce on the disorder – the Tyrells are going to keep looking for potential converts from lords and landed knights on the borders, the Tullys are definitely going to want to grab the Golden Tooth if they can, the Greyjoys would definitely be interested in Fair Isle or some of the coastal castles.
And then there’s the problem of royal disfavor. Aegon V has already had to come over to the Westerlands three times, so there’s already an understanding at court that the Westerlands are a problem area. Now they’re dealing with a bunch of usurpers, and the Targaryens don’t want people to get the idea that just anyone can make themselves a Lord Paramount without their say-so. So King’s Landing is going to respond with increased central government at the very least (more royal tax collectors, more inspectors and auditors, more royal justicars) and may go as far as declaring them rebels and outlaws and naming another house to replace them.