I have never seen a therapist in their home. The ones I have seen have all been in an office with no secretary or staff. Just the therapist's office and a waiting room in a building. I probably lean more towards finding not cozy better.
I don't think I would like going to their home office. I saw one for a very short period of time who, along with a couple of other therapists, who rented an apartment and had made the rooms into individual offices with a common waiting area in the apartment foyer. I thought it was awful because of all the other people around. They did not have a secretary either - they were all sole practitioners who shared space.
The one I see describes her office as warm and inviting in her blurb on the internet. I would not describe it as such, but it is not especially offensive except for the awful couch and lack of a chair as an option.