All without having the need for a police cordon around the crash jumping on pax with bags - a
PR 'optic' that the airline may wish to avoid.
After the first two occurrences make the news the urge to take bags with you will go down. That 'optic' is exactly what is needed to change behavior.
Also there is no need to jump on the passengers just firmly take the bags, offering a receipt in exchange for passengers name.
I suspect in most cases the passengers will not be able to simply walk away, for safety and other reasons they need to corralled anyway.
BTW: Totally agree with the other points, especially on taking 'real' responsibility for PAX property.