Another issue to me is that not everyone knows how to harvest from a garden. They may not know when something is not ready or they may destroy the plants while harvesting. Not that they do it maliciously, they just don't know any better. And you have the risk of a vandal, someone that would destroy everything just for fun. I don't think opening it up to the neighborhood would be a pleasant experience though some of the people you net would be a pleasure.
Exactly this! That's why supervised visits are a great idea. Take my sister, for instance, who has been around gardening for years but never really undertook to educate herself on it. When she suckers tomatoes, she twists, yanks and otherwise tears any branch located in or near the juncture of another branch of the vine. Mother and I have watched in horror, as no matter how many times we show her what a sucker looks like, she just rips and tears.
We no longer invite her presence in the garden.
And my DIL, who claims she has gardened all her life, but ripped out all the perennials I had bought and planted in her garden, while leaving the weeds behind...and still doesn't know one plant from another, when to pick anything or if it's even ripe for picking, or just anything to do with gardening.
If you truly want to grow food for yourself and others, you can approach it one of two ways....the "oh, well" approach of just letting folks come and go, do as they please and hope for the best. Or, you can put a little more work into it by treating your garden like a food bank and educating others to do the same. I take the latter approach, as it's not just a hobby to me, but a way of providing my family and others with healthy foods, not only in season, but for the winter months as well.
If it's just a hobby or a nice gesture, let them roam at will, but if you truly want to provide food for others, it would be more efficacious to educate those participating and monitor the use of your garden.
Another alternative is to designate rows where you don't care if folks wander in and pick whatever and then reserve space in the garden for serious food production.