1,000% agree here with all you said. I am not a "my pet is better than co-workers" type of person necessarily. However, I do see your point. And the focused work is what I have liked over 6+ years working from home.
I do find that relationships and getting to know co-workers and managers and their quirks and likes/dislikes takes more work. The other thing I have noticed time and again: if it is mixed work-from-home and work-in-the-office, then the side conversations and pop-bys have to be documented and shared across the team somehow. This way people know what is going on, why, how, who talked on it and are not left out.