This is from an Advisory Circular from the FAA in 1993:
Use of Portable Electronic Devices Aboard Aircraft - FAA AC 91.21-1

"(6) Prohibiting the operation of any portable
electronic devices during the takeoff and landing phases of
flight. It must be recognized that the potential for personal
injury to passengers is a paramount consideration as well as the
possibility of missing important safety announcements during
these important phases of flight. This is in addition to
lessening the possible interference that may arise during sterile
cockpit operations (below 10,000 feet)."

As it is there's not way for FA's (who are charged with enforcing cabin safety FAR's) to determine the type, function, operation of any and all possible PED's at any given time. As a blanket rule it's required that all Portable Electronic Devices be turned off for door closure in order for the pax to not be distracted from any and all safety demos. Before cell phones people were much more compliant, they seemed t hear more of the announcements we make regarding time until door closure, stowing baggage, putting seatbacks and trays up etc. Not everyone is distracted so it's not uncommon after 3 or 4 announcements to then have to walk through and make the same requests to 5-10 people once again. I always ask nicely but sometimes am not met with the same respect.

Even if you don't pay attention to briefings, they are required and not everyone is ignoring the information which could be useful were there an event. This is why they aren't allowed on taxi-out. BUT, as stated, during longer delays and ALWAYS ALWAYS after the demo and cabin checks I've had the CA authorize PED usage.... getting people to turn them BACK off is a whole other uphill battle : )