No business has a legal obligation to make a profit, that's just nonsense. It just means the CEO isnt held accountable for the inevitable losses. However more importantly here, running tax-exempt frees the stores from the crushing burden of taxes, which might just provide sufficient margin to make it possible to survive in this crazy business model.
Ever hear of St. Roger Abbey Patisserie? I went into a mall yesterday and saw this store. I went in to get a croissant, and there were Nuns behind the counter waiting on people. It’s not “pay as you can”, but it looks like the money is for their order and to help the poor. Cool.