Heck, in many companies I have encountered that they don't even know who is using API keys they've issued to third parties, especially over generations of systems. I am impressed that after getting email approval for an app a decade ago, Yelp still had contact details enough to let the O/P know!
None of that negates the issue of 4-days notice and Yelp shooting themselves in the foot by removing access to an app which redirects people to their website. But someone in executive management made a decision on the basis that they wanted revenue from the API overhead, wanted a slice of other people's pie and that's that.
To the O/Ps point about subscription, there was a UK food app which gave you restaurant food safety scores taken from the food safety agency "Scores on The Doors" it's gone now but I paid a few £ a year for it and never had an issue. If the Yelp pricing is sustainable at that level it's not a bad idea to pay for API access, Yelp has to pay for their servers and a portion of the API calls won't be converted to traffic. Who knows if Yelp still has a sustainable business? Maybe that API thing doesn't pay for itself? I don't know.