I think it's also insurance reasons too. If the aircraft suddenly moves and the seat belt sign is on and the crew have mentioned in their PA to stay seated and you hurt yourself, you don't have a leg to stand on(pardon the pun) Its the same with turbulence, really makes me angry when parent wont secure their wee bundles of joy "cause they don't like being strapped in"
Know of one case were the passenger knew better and wouldn't fasten their seat belt in turbulence and ended up badly injured and is now trying to sue the company
If crew are injured carrying out their duties they are insured by the company.