The broken windows theory isn’t about violent crime, it’s literally about property crime and offenses like vandalism. The idea is that when that kind of petty crime goes unchecked, the crime situation in the area spirals, both in terms of quantity and severity, eventually leading to more violent crime.
You can disagree with the theory all you want, but to assert that the issue is that it should only apply to violent crime is to fundamentally misunderstand the assertion the theory is making.