I don't think that's completely unachievable with the current state of NLP tools.
You could (roughly) measure the diversity of discussion topics, the frequency of positive and negative emotions, etc. It'd be work to do it well, but I think it could work decently.
You're suggesting that you can find things you assume correlate with what people want out of a community, but several people here commenting they can't define what they want. There's low odds of it somehow matching what they want, but struggle to express.
You could (roughly) measure the diversity of discussion topics, the frequency of positive and negative emotions, etc. It'd be work to do it well, but I think it could work decently.