Richard III I think is a different case - he's simply supposed to be a lousy person, not an okay person with one tragic fatal flaw that will destroy him and everyone around him. You're supposed to love to hate him.

With Coriolanus, I think you're supposed to go "Wow, he's so brave and valiant and noble! Pity he's also as proud as Lucifer, as that undermines his other outstanding qualities and eventually makes him a traitor." A modern audience may not feel as enthusiastically in favor of conquest as an ancient Roman/Elizabeth English one, though, so "He's so good at vanquishing the enemies of Rome!" may not hit in the place where it was intended.