Canadian physician here: yeah, this is hell for us trying to reach patients through the hospital system, which is "unknown" by default. Straight to voicemail and you can't really leave a message.
Totally agree though, this problem is very time consuming, if only for the time it takes me to look at my phone and decide not to answer the call - a few seconds of my life each time. My worst day was a few days ago; 7 calls.