"My aeroplane, My radio and Your checklist".
So you have two separate operations going on in the cockpit: one flying, getting (probably quite critical) ATC instructions, as well as making instant snaps about where to head, levels and the other head down going thru the QRH (with no interruptions).
That is not necessarily better CRM, not to mention throw in "that switch is in your area of responsibility, turn it off will you?".