What seems to make SF pretty unique is that even in the wealthy areas it lacks effective law enforcement.
Also, poverty in Mumbai isn't quite the same as poverty in the rest of India. Significant portions of Mumbai approach US-"poor" levels of income (about $15-20k/year, PPP adjusted) which is considered quite wealthy over here.
Where I live thieves are often beaten to death. And the rate of theft is still high. I could point you to some studies about punishment not being an effective crime deterrent, but not sure it would change your mind. It's a complicated problem and law enforcement is a band-aid at best.
Fundamentally I think law enforcement is just one piece of the puzzle. Intrinsic factors (culture, biology, economics, psychology) also play a major role - all else held equal, the US is likely to be more violent than India (important exception being sexual violence). But law enforcement does matter - how else to explain how clean little India is in Singapore and Kuala Lumpur?
I'll certainly look at your studies.