Whereas the severely limited self defense options of places like Australia strongly favor the criminals.
And yet, crime rates in Australia are FAR lower than those in the US. Suggesting that your beautiful hypothesis is unable to defend itself against beastly facts.
Some crime rates are lower, and it leads to a case where the aggregate rate is lower. But some types of crime rates are higher - rape, assault, and burglary are higher per capita in AU than the US.
Intentional homicide rate, Crime levels, Rape rate, Murder rate per million people, Murder rate and 78 More Interesting Facts and Stats
www.nationmaster.com
It's very difficult to compare an overall crime rate when the laws are different on certain things. AU's gun control will absolutely result in a lower crime rate for all things that involve guns - duh. Similarly, the ease of acquiring illegal drugs results in different offending rates where drug use is involved (not necessarily just direct use or possession crimes).
I'm not saying that the US is better. We have many, many, many problems. I'm only saying that a high level comparison isn't really useful, nor is a simple "gun control!" proposal a viable solution to the problems that the US has. US problems are not the same as AU problems, it's not reasonable to think that the way AU addresses issues is the best way for the US to do so.