That's interesting. Here in Berlin there is/was also a restaurant where you could pay what you want when you leave and it seemed to also work there. I can imagine important is to explicitly state that you do have costs and are expecting payment - it's just not such a strict thing and if you are a student of course you pay less. Let's see how it goes.
Agreed. I got the idea from the Humble Bundle[1] and wondered if it could work with physical products as well, instead of digital. Turns out there are more businesses than I thought doing it, even in the city I live, although it mostly seems limited to be coffee shops and restaurants for some reason.
If nothing else, this experience showed me that people can be pretty generous if you give them the chance, which changed my outlook on life for the better.
I may try offering a plan with this model for a limited time on my hosting business, to see how things go, as an experiment. It may be a little difficult since dedicated servers are not cheap, but depending on how much each people pay, it may offset the costs and turn into a profit. Tom Morkes[2] has a book on this model that might be worth the read as well[3].
Personally, I go with no analytics whatsoever for my business, for personal reasons, but we do offer a GoatCounter to customers to entice them to move away from Google Analytics. I will definitely keep an eye on Counter.dev as an alternative to that, good luck!