The threat of violence from police and incarceration by police are also associated with the presence you mention. These also prevent crime from happening.

The “problem” is that it’s physically impossible to have police everywhere, all the time, for that prevention to be meaningful. It’s diminishing returns and exponential cost. So programs to prevent people from turning to crime, like jobs programs, pay so they aren’t suffering in poverty, affordable and accessible mental health and regular health care, addiction treatment, decent housing, etc. are the logical next steps.

But no. We just hire more cops, give them more guns, and the equivalent of military armored vehicles. They choose violence.