Interesting post. I was a bit confused why they were seeking to build rapport with their users. These people pay a few bucks a month. What's the upside to a close, cosy relationship?
The answer might often be to understand the users' needs better in order to design for it. But OP seems to have a clear idea of how the app should work already. So...unclear.
I wouldn't use the word cozy but in theory loyalty, evangelism, retention, word of mouth would all improve if people had great experiences and felt like I was accessible and responsive, and this might be transferable to other projects, etc. And of course I talk to users to understand their needs, just doesn't mean I implement all their ideas.