There are so many problems that are solved by ones own money, and people not being jerks about it. I think a lot about how some bus stops will just have chairs that people leave there to offer seating when the city decided not to put any.
In your example, the person who left out the chairs isn't worried about being paid back for the chairs. Someone has excess, they shared it freely without expecting anything in return, and the community is better for it.
The "socially-enforced expectation" is the same. You know whether you're doing something altruistically for the common good, or whether you're doing it because if you don't others will try to shame you.
As soon as you introduce coercion, the type of people motivated by power are attracted to the power to coerce and corruption takes root.
Typically there's a cultural expectation of "wellbeing for all", which becomes a significant social expectation. If it's the cultural standard, it changes the relationship to chores significantly - I can contribute to them knowing that the general person out there is also doing chores with my wellbeing in mind.
If I understand you correctly, mutual aid theory explains the author buying cheap forks just to do something good. At the same time, in the absence of penalties people will steal forks until barely any remains. So why should one believe that the balance will favor the fork buyers more than the fork stealers?
Ask yourself, why would you take more than you need? Not some hypothetical other person, but you, personally. Do you think other people are in general likely to behave like you? (Put another way, do you think you are fairly typical when presented with a "take what's fair" scenario?)
It's like the candy bowl at an office or someone's house, or the "take a penny" cup at a store. I'm sure occasionally someone takes everything from it, but by and large people take what they'll personally use.