Dealing with an answering service seems to me to be a bit like part of a contest for control.

I call you when I feel like chatting, but you make yourself unavailable.

And you call back, if you do, at a time when you feel like chatting.

It’s not conducive to a feeling of being in contact. More a feeling of a being the loser (or winner).  I don’t have an answering service turned on. If you ring me, you get me. Sadly, you don’t (ring me).

As you can see, I don’t even know what it’s called now. Voicemail, maybe.