First of all, thank you for coming up with an original topic for discussion! I don't think I've ever seen this one before.
Personally, most of the phone call instructions that I receive from my doctors don't really bother me. Most of the time they're either calling to tell me that some lab tests were normal, or that the doctor said to continue taking prescription X, Y, or Z for 10 more days. That kind of thing. Nothing really horrible.
The few times that I've received some bad news over the phone have all really involved my insurance. Getting a call that says your insurance has denied coverage of some procedure, or that you need to get another pre-authorization for your prescription is not pleasant news. It usually means I need to get on the phone and fight with my insurance to get them to cover what they should cover in the first place. But their usual policy is deny first, then make the patient fight for their rights.
The phone call that I do actually enjoy is the one reminding me of my upcoming appointment for a full physical exam. When they call for that, they remind me of the purpose for the appointment ("we have you booked for a complete physical exam"), and also any prep and fasting instructions ("please don't eat or drink anything after midnight" and "don't apply any creams or lotions the morning of the appointment"). Those kinds of calls help me to look forward to my exam!