I've seen people on multiple flights in the 90s using camcorders and digital cameras and such during take-off AND landing, domestically AND overseas, and not once did the flight crew say anything in person or on the PA.
Maybe they're afraid a recording device will capture contentious or newsworthy footage just prior to a crash, depriving the airline of the chance to put a lid on events. Imagine an intact, functioning passenger device capturing the final 45 seconds of spins, aerobatics, and the terminal dive or mid-air explosion only to land in a cornfield or in someone's garden, and ending up on the news after the airing agency makes a pristine copy prior to handing over the original to the FAA and NTSB.
I declare NOW that if my device ever is found and suspected of having informative crash footage, my device may be and can be copied by any civilian, news-apprising party so long as only the news bits get released.
I am not saying impede a proper investigation, but some of them take way too damned long to be publicized, and often the public short-memory-effect works to the advantage of the industry and investigators who don't want pressure to find a cause quicker than they are comfortable with. OTOH, if someone has a film camera and captures footage of a plane from nearby crashing, it seems okay (or not contested) that a TV station gets footage on the air pronto. I don't EVER recall seeing any print on a ticket saying I and my property may be seized to to aid investigations.
If none of that is the issue, then what is? Passenger electronics aren't that powerful to bring down a plane. EVERYONE would need to be simultaneously running them, and possibly actively running illegal transmitters of some kind to really start messing with the plane. Maybe they just want to be in a commanding position to demand everyone's attention. That in and of itself is not bad, but once the safety announcements are made, it should be permissible to fire up one's gizmos if they are low-power like phones in airplane mode, calculators with no real Bluetooth power, cameras with no transmitters or satellite links, and laptops with the antennae turned off.