I see a possible solution here using technology:

Senders should add a small $1 "black box" recording acceleration data, and shipping companies should be able to query for a certain package and a certain timestamp, which employee was accountable at that moment.

Then when you receive a broken package, the black box tells you the timestamp when it was thrown to the ground, you tell that to the shipping company, which then finds the employee at fault and gives him/her a warning/sacks him/her.