When I encountered these they were maintaned by a community or space like houseprojects, collectives or free shops. Some seemed to be accessible all around the clock and some just when the space was open. So its not just a fridge standing around but actual groups/people caring for it.
Don’t get me wrong, it would be great if it did. But, people aren’t going to put labels or clear it out. It would be a well-intentioned, gross health hazard.
I think there could be inspections done regularly (every week or month) by the owner of the fridge or by other people (depending on your idea of how the fridge should operate)
I can see it working in more rual areas where people all know each other and all grow a bit in their garden, make their own products at home and share this way. Can't see it working in any city, at least in the UK.