Believe it or not, but I'm generally a pretty pleasant person. But when somebody adopts an formal impersonal tone like NVC, they make it clear that they don't see me as their friend and that I shouldn't consider them my friend either.
As you said, NVC is good for 'forcing people to do something they don’t want.'
NVC does not mean using a formal impersonal tone. NVC is about content and context. If people are using a formal tone with you it’s for a variety of reasons—maybe that’s the appropriate tone, maybe they are frazzled and meet a framework to express themselves, and maybe they’re simply bad at it.
I’m not sure why the “not a friend” part comes into it. Most people I talk to are not my friends. When people who aren’t friends treat me like a friend, it is creepy and alarming.
NVC is factually impersonal and formal. Instead of having a genuine human interaction with somebody, NVC aims to lay out a method of choosing ones words carefully to influence the receiver in the desired way. Nothing about it is casual nor genuinely personal, no matter how many times you utter the word "feel".
Feel free to substitute "friend" with "somebody you treat pleasantly with the typical degree of respect". A manager who uses NVC is little different from a used car salesman who gives firm handshakes and throws around warm smiles.
I think any communication technique that you are just starting to practice sounds unnatural.
Just think of NVC as a tool in the toolbox, for how to initiate a difficult conversation and be understood without being as likely to provoke a defensive or derisive response... that then can grow into that genuine, comprehensive human interaction.
As you said, NVC is good for 'forcing people to do something they don’t want.'