I'm guessing your way is most applicable when working a relatively low number of hours, like 35-40 weekly. Once you start pushing into 80-100 hours at work each week, being friendly starts to make more sense, if only to avoid going crazy from isolation.
Once you start pushing into 80 hours you need to forget about making friends at work and find another job. It's inhuman.
no this is the best policy for a normal job. You are not isolated, you are working. That means a good deal of communicating with coworkers, but about work, not about personal.
I my experience having lunch with colleagues helps to get to know your co-workers. Which in turn helps to work better with them. Usually they do not become my friends. It is still a professional relationship.
I am curious: Are you going out for lunch alone? Or are you not going out for lunch at all? Or don't you have a lunch break?
Work doesn't need to be about buddies. work is about work. That's why you have a personal life. keep the two separate.
corollary #1: dear manager. I am not your friend, you are not my friend. i will never be your friend. Chances are i don't like you at all. Just be professional, and i'll be fine with that.