I've noticed that many fans (even here) seem to forget that when Gandalf told the Witch-King to go away, the Witch-King laughed in his face, called him a fool, and drew his sword. Rohan wasn't an excuse for the Witch-King to run, Rohan was an interruption in the battle. The Witch-King left to support and save his army, and Gandalf wanted to make chase so that the Witch-King wouldn't do what Gandalf was trying to prevent, said deed being protecting and leading the army. The Witch-King did not cower out. Aragorn, Legolas, Faramir, etc would all have done the same thing if enemy reinforcements arrived, causing panic within the troops.
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"And forth went Morgoth, and he was halted by the elves. Then went Sauron, who was stopped by a dog and then aged men. Finally, there came the Witch-King, who destroyed Arnor, but nobody seems to remember that."
-A History of Villains
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