As I said in a post that got pulled a lot earlier but has been repeated here. You want pax to check bags and not take those smaller bags with _very_ valuable contents?
1. Reduce or eliminate checked bag fees.
2. Actually take care of pax's bags.
3. Take accountability for loss of bags far more seriously
4. Understand that the cabin bags now contain things of considerable value to the pax. So ensure that #2 applies to bags left in aircraft after an evacuation. State that the bags will be guarded - and guard them.
5. Provide cheap money belt/wallet holders that can carry wallets, passports, money, jewelry, phone etc. and which are completely hands free.
Those 5 steps will reduce the need for pax to want their bags it will still not fully answer the problems of 'parents' ashes in the bag' but it should improve things. 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.