The only obvious explanation I can see is that they don't like the way it reflects on their image within their customer community.
I imagine it would be similar to unwittingly having someone set up a GoFundMe page for me as an individual. "Hey let's all help this guy out!" Sure, it's free money, but at some cost to my reputation with some people who would consider it a sign of weakness.
Yelp is implying a supportive relationship that does not exist.
Quite the contrary - jwz does not want his business listed on Yelp. He does not like Yelp, and his blog describes some of the issues.
(Eg, Yelp requires/d "a photo in which your whole face can be seen" while DNA Lounge wanted to use "our logo as the image" - quotes from jwz's blog.)
How would you like me telling everyone that "I'm frank_nitti's best friend", and (honestly) raising money for you, when you don't want me in your life?
What happens if an alternative GoFundMe site, auto-generated by Yelp, results in a reduction of the overall donation stream? Then it wouldn't be "free money", would it?
So, who decides if this plan is appropriate for the business?
I think the opinion restaurant owners have of yelp ranges from dislike to outright loathing. Yelp has the reputation of being a bully and essentially extorting restaurants for money. Most of the negativity is probably because of that. If it were someone like Google doing it then there'd probably be a lot less outrage.
I imagine it would be similar to unwittingly having someone set up a GoFundMe page for me as an individual. "Hey let's all help this guy out!" Sure, it's free money, but at some cost to my reputation with some people who would consider it a sign of weakness.