While some fraction would then escalate to rendering their victims unable to shoot prior to approaching, I think a greater fraction would simply choose a less confrontational way to acquire spending money. Those who did not change tactics would eventually get shot.
If the prey people change tactics, so will the predator people. Shooting the muggers tends to produce a wilier, more dangerous, harder-to-shoot breed of mugger. There will be fewer of them, but instead of waving their knife in your face, they will bash the back of your head with a rock. While you are out, they will photograph everything in your wallet before putting it right back in your pocket, and take just your phone and gun. Then if you don't report all your cards as stolen, someone buys your details from a darkweb site, does a little social engineering, and cleans out your accounts.
If you could somehow automate the process of stealing just a little bit of money from a lot of people, all at once, all the time, that would totally disrupt...
...the banking industry.~ [cue rimshot]
Thank you. I'll be here every open mic night.