Earlier quoted context omitted.
It depends on the community. For this one, it's a bunch of folks learning to code and getting coding jobs; I can imagine many of those ending up working at tech companies who might be great Slack customers, and evangelising because they had such a great experience using it - so the investment of supporting a 'free' chat room could pay off over time.
I don't know if that makes long-term sense. The OP sounds very entitled: "We'd endorsed Slack to thousands of people on our Twitch.tv streams, and even mentioned it in interviews with the media." Of course Slack must provide them with free chat rooms in perpetuity, they've even been mentioned in interviews! It's probably better to be rid of "customers" like this sooner rather than later.
Agreed. This is more or less an example of patio11's "pathological customer": they won't or lack the resources to pay, have an unreasonable use case and overinflated expectations, and proceed to throw a fit loudly and publicly when they don't get their way.