Overzealous Pickers and the Commons Problem

Seattle is establishing an urban forest for foraging food. Say what you will about grocery stores, but they do a nice job of allocating scarce resources (food). I'm not  sure that the urban foraging forest will do the same. Perhaps most concerning is that the "overzealous pickers" are expected and the expected solution is to simple grow enough food to meet demand:

Of course, any "free" food source begs the question of what to do with overzealous pickers. No definitive answer on how to handle that predicament has been established yet, though. According to Herlihy, the only solutions right now are to produce an abundance of fruit so there's enough for everyone and to embed "thieves' gardens" with extra plants in the park for those people eager to take more than their share.

So what is the expected demand for food when P=0? The commons problem cannot be overcome by providing more goods for free. You can't grow your way out of overzealous picking.