Why do some U.S. airlines require passenger headrests to be lowered during takeoff?
The answer appears to be one of clearing the view of the flight attendants. This FAA circular mentions the requirements that a FA be able to see clearly.


  (3)  Direct View.  As used in § 25.785(h)(2) [§ 25.785(h)(1)], "direct view" means direct (line of sight) visual contact with cabin area/main aisle(s), which enables the flight attendant to be made aware of passenger needs relative to safety when the flight attendant is seated with torso restraint (safety belt and shoulder harness) fastened.  Mirrors or other such devices are not acceptable equivalents to direct view, except in those cases where flight attendant proximity to the floor level emergency exit takes precedence over direct view.  Video systems may be an acceptable means of direct view, if the level of conspicuity is equivalent to that provided by line of sight visibility.


This forum thread talks about it with regards to FA regulations


  I have been told by many FA's that the reason for the headrests to be down is for FA visibility during takeoff and landing and taxi when they are in their seats. With them up they don't have a clear view of the cabin.