I do most of my shooting 2-eyed, but sometimes - and only when target shooting - I close the off eye when I really want to bear down and put that arrow dead center X. Like when I'm having a nock bustin' war with some of my shootin' buddies.
Oh... I don't guess many people do that any more. Hard to do with carbon arrows without busting out the back end of the shaft or robin hooding the blasted things. One more point for aluminums with nock tapers.