Having your lead hand down is proven not to have any effect on your ability to defend punches and people need to stop talking about it.
Rofl I was almost going to rep you for this, then I realized you're actually serious. Iunno maybe try sparring sometime using only head movement. It could work.
Marcus Aurelius: Tell me again, Maximus, why are we here?
Maximus: For the glory of the Empire, sire.
Baked, not fried... the healthy choice.