I won't use live coding questions (usually) because I don't see much value in trying to code under that much stress.
But I will ask hard questions to see how well a candidate communicates in a stressful situation (which I think is a far more valuable indicator of their brain's "default" mode in stress). I want a candidate that talks honestly about stuff -- especially the stuff they don't understand -- even in a stressful situation. Sometimes stress can bring out the asshole in somebody -- and that's an immediate red flag.