Personally if I'm in a waiting room, I'd rather not have to have a conversation with strangers there. Whether it's waiting for a therapist session, a doctor appointment, etc, there is usually a sense of dread or introspection to one degree or another. Most people are worried or at least have something on their mind. Some might like to relieve that with chit chat, but I'm not one of those. I wouldn't welcome someone striking up chit chat with me. I would want to just sit quietly and think my own thoughts, or read something.
I think it's okay for people not to chat with strangers in a waiting room situation. While it's also okay if they want to, at the same time it's okay to not do that, the same as on public transportation; most people are fine with just sitting pretending they're alone in a crowd. But then, I live in a major metropolitan area where if you chatted with everyone you found yourself surrounded by, nobody would get anything done in their day, as we number 10 million and you have to get a privacy bubble around you just to get through your day.