Overweight baggage resulting in overhead lockers opening during landing

The reporter expressed a safety concern relating to the security of the overhead lockers and the size of the bags which were allowed as carry-on baggage on a recent [operator] flight from [location 1] to [location 2].

The reporter advised that before the flight departed, a passenger opened the overhead locker to place a coat inside and a large rucksack fell and struck another passenger across the aisle who was carrying an infant (the infant was not struck). The crew had difficulty closing a number of the lockers and had to get help from a passenger to ensure they were closed properly. Some of these lockers contained bags, which it appeared would normally be considered too large for carry-on baggage.

During the flight, another mother had to open several overhead lockers on a number of occasions and on each occasion had difficulty reclosing the lockers due to the weight of the bags inside and the need to reach high overhead to press the cover against the latches, often resulting in only one latch being engaged. The crew also had difficulty closing the second latch and did not always succeed. During the very gentle landing, these partly latched lockers actually remained closed but the rucksack which had caused issues earlier again fell from the overhead locker, which had reopened, and struck the passenger beneath.

Reporter comment: Had we struck serious turbulence during the flight a number of the overloaded and partly latched lockers would most likely have opened and very heavy items would have been unrestrained in the cabin. This could have very serious consequences. Presumably, there were other partly latched lockers outside of my narrow field of view, so the potential problem could be greater than my own observations suggest.

Do [operator] have a carry-on baggage requirement and is this enforced at the various international airports they operate?