If a person has their keys in their pocket, they can get in the car and be out of sight and get home or to the police. The robber will probably have run blocks away before looking in the purse and tossing it in the garbage.
And then he'll go rob some other lady, maybe one who isn't quite quick enough in giving up her purse. Then she gets knocked on the head, and maybe has a brain injury.
Giving them what they want only encourages them. They must be stopped.