Oh I think being available... and providing a way to contact is quite professional. What I was referring to is giving out your home number to patients, and allowing them to call you.
My pain T calls me within 5 minutes usually when he isn't holding office hours, and in his next break if he is. I can leave all the messages I need to, and even fax if I wish. He doesn't email, but neither do I.

I have all his numbers, home, cell, his wife's cell too? because I have them for my phone with a special ring (I don't answer my phone when I'm in pain flare so I need to know when it's him) but I have them listed as DNC (Do not call!) for myself.
Even so, I would never call him on his personal numbers... well, never is a long time. I think right after Hurricane Wilma, and so many phones out, he did have me call his home number one time, but that was HIS direction.
For those new Ts without any answering service of their own, IDK. If you have a cell phone, and voice mail... and on a particular weekend the client is really having difficulty... IDK you have to make your own decisions.