there’s no law against being a bad neighbor

There is in many (most?) cities - every one of these is against city ordinance where I live. It's better these sort of things are handled by the city; applied to many more people it's harder to pull grass-measuring or other shenanigans.

rabbits that live under them and eat your garden.

Rabbits do not need cars to eat your garden, furry little buggers are perfectly happy with a hole anywhere in the ground. The excuses against 'car guy' are always the weirdest, especially the HOAs that don't even let you do basic oil changes yourself.