Is avoiding bias similar to a fat person avoiding cake? I don't doubt fat people generally want to lose weight but they avoid all the deliberation that would prevent poor choices. They're aware their will fails when directly tested and yet they don't take simple actions such as planning out healthy grocery lists in far mode. Anecdotally, I see the same pattern with people that know of biases yet while time and again failing to avoid them (Kahneman, even).
It's kind of amazing. It makes Odysseus tying himself to the mast of his ship to avoid the influence of the Sirens' song seem implausible. Still, a small percentage of fat people do somehow succeed.
I think it's pretty significantly unlike a fat person trying to avoid cake. At least when you fail to not eat cake, you notice. One might be able to hold to a restrictive diet by sheer willpower, albeit with great difficulty, but bias can't simply be willed away.
An example of real world problems from cognitive biases:
Forensic science - Ignorance is bliss
Hat-tip to Bruce Schneier.