The bold "pay-what-you-want" restaurant experiment
salon.com
salon.com
This is the crucial point. The Radiohead model is not applicable because for them the albums is a publicity machine that feeds into their real business: concerts, memorabilia, etc. Think Google, every free service/tool/platform they offer funnels into their main search business.
I think for big chain restaurants, like Panera, this may make sense. The loss they suffer from 2-3 stores is more than offset by the huge publicity they gain, but they cannot do it widely. For small unknowns it doesn't make sense to do it continuously but they make try it for short periods of time. Similar to how small businesses tolerate Groupon's huge 50% commission.
Doing this as a short (e.g. 2-3 month) experiment also gives you an excellent indicator of the perceived value of your service.
It should be noted that in Berlin, you ride the underground on something of an honor system, and no one j-walks, so the culture clearly supports this kind of business model.
Make it a place where you take your girlfriend on payday, and it will be a total success.
It totally depends on context.
Radiohead makes money if the average price paid is more than the average bandwidth and hosting price. And hosting is very cheap nowadays.