Why didn't King Robert wipe out the Iron Born?

[Sunni]

Robert didn't wipe out the Greyjoys because, once defeated, they posed little threat.

Robert wanted to wipe out the Targaryens to prevent their followers from (eventually) mounting a rebellion to put them back in power. The Targs have a legitimate claim to the throne of the Seven Kingdoms. Many houses of great means support them. This is not the case with the Greyjoys. They have no legitimate claim to the throne and are unlikely to win the support of other well born families in Westeros. In fact, as reavers, the Greyjoys are despised far and wide. The threat they pose to Robert Baratheon is completely different from the Targs and easier to counter.

Robert was admittedly weak on planning, particularly on planning what might happen after his death. Still, he wasn't worried that the Greyjoys would turn his subjects against him because they never could. And he wasn't worried that they would take over and hold the Seven Kingdoms because they lack the strength, (even Asha saw this) which was proven by the events in ADWD.

[seeyouintee]

I think Robert's personal vendetta against the Targaryens (which was probably exacerbated by the closed council and especially Lannister influence) had a lot more to do with him wanting to wipe them out than any claim to the throne. Aside from Targaryens, he was pretty forgiving.

[Jon Flowers]

It has been pretty well established in these books that one of Robert's few positive moral qualities is his magnanimity towards defeated enemies. It's just part of his personality. In most cases his generosity worked out well for him, after he had beaten the Storm Lords and Ser Barristan for insance. This in no way invalidates th perfectly plausible explanations put forward by others. Disparate motivations leading to the same end can certainly dovetail with one another