I had a friend start shooting a few years ago, and he followed my lead, shooting in his yard. The first day, he called me and said, "Hey, how far do these arrows go?"
He had accidentally shot an arrow OVER his house and off into the subdivision. I feared the worst for him, but he never found the arrow, and never heard from anyone.
A few years ago I was shooting broadheads and had a 3-blade plane off-target, and lost it in the grass. I have nearly 3/4 acre, and could shoot up to 80 yards safely if I wanted to, and was shooting the broadheads in a pretty safe setup. But I have had arrows slide through the grass into the neighbor's yards at times, and it was of extreme importance to me to find that arrow before anyone else did. After 2 hours of fruitless searching that night -- by flashlight after the sun went down -- and 2 more hours at dawn (before I had to get to work), I found it. Now I only shoot broadheads from the end of my driveway into the back of the garage.
Accidents DO happen, and lots of stories and pics are here on TG attest to that. Weird releases, skipping off the top or sides of targets, nocks breaking at release, bowstring catching on clothing and arrows flying weird... that's bad enough when you're NOT breaking the law. I know how it feels to push the rules and get burned bad, and those ordinances are a pain and some are rarely enforced... (I mean, should we really need to get a permit to install a new water heater?) But if something bad happens, or your neighbor's mother-in-law stops by and complains because she thinks you're endangering her grandkids, and a LEO with a bad attitude rings your doorbell... you're going to be at the mercy of the system, and the consequences won't be up to you.