yes with less cash there will be lesser cash robberies and death, but eventually this criminals will adpat, and may target that are openly involved in bitcoin transactions like maybe a store that says it accepts bitcoin
People will still mug others. They would still your phone because they would know that you had a Bitcoin wallet installed on your smartphone. Fake stores are already a thing, mostly on the Internet and many people got scammed in a such way.
The biggest advantage is that we won't need ATMs and banks where you can deposit and withdraw money. Less risk for people who work there.