Great question. Maybe markets aren't a functional solution to problems of public commons? I can't think of a community problem where a market-based solution even helped, let alone solved the problem.
While I agree that the market isn't the panacea and God it's portrayed to be, I didn't understand the GP that way.
Your point goes much too far the other way. Most of most community problems are solved by 'free' markets, including food (most food is bought and sold in the market), much of transportation (cars, planes), shelter (most homes are owned by private parties), etc.
I think the interesting question is, where is the market good at, and what are other tools good at?
That's shifting the goalposts and not what I said. They are mostly solved (along with other issues) by free markets. Most people get their food and shelter that way, and the market generates most of the wealth needed to feed and shelter the others.
Free markets have a great time servicing 80% of the people with 20% of the resources and then pocketing the rest of the resources as profit. Community solutions need to be able to service 100% of the community. It's like the "last mile" problem of economics. "Sorry, it's not profitable for the police to protect your neighborhood" is unacceptable.