I think it’s an interesting approach, but I can see two ways it can go wrong.
The first issue is price signalling of some sort. The customer has to have some way of knowing what a fair price for the product is. One of the reasons that a cafĂ© is an excellent testbed for this is because the ubiquity of Starbucks has taught people that coffee drinks cost $3—$5—and it’s possible for a savvy entrepreneur to cut operating costs pretty substantially so as to be able to make a profit if the average coffee price is $3. Meanwhile, the customer thinks, “This would cost me $3 at Starbucks, and this is an independent business doing something cool that I want to support, so I’ll throw in $4.”
On the other hand, there’s a tea shop near me that sells an incredible variety of teas. Some of them are available at Starbucks prices, but others cost four or five times that much, because of rarity or labor-intensive tea farming. Without some kind of a price board, how can you signal to the customer that this is an organic estate Darjeeling that costs the shop $5/ounce, and that is a blended tea that costs the shop $1/ounce? For the organic small-estate Darjeeling, I’m not bothered by paying $10 for a pot of tea; for the blended tea, a fair price is closer to $3. Now, I’m a tea snob, so I know what the price ranges are; but how is a tea novice who just knows it all tastes good to know that if he offers $3 a pot for the organic small-estate Darjeeling he’s making the store take a loss on that tea?
The other issue would be freeloaders. This is a huge cultural difference that I’ve observed in my trips to Europe—Europeans take a more collectivist attitude towards things, while Americans take a more individualist attitude. The system can support a certain number of freeloaders, because some people will pay more than the product costs, but if there are too many freeloaders, the people who are paying money will think it is unfair. In Europe, this would result in social pressure to not freeload (and to only pay less if you genuinely can’t afford it); in the US, I think it would return to a fixed price system, if it got abused.
But I don’t see why it wouldn’t work, even in the long term.