I have had this voicemail issue with my iPhone 7 Plus 128GB since November and I have swapped the phone at Apple store 3 times already. I have spent so many hours back and forth with probably 10-15 Apple advisors, sr. advisors and Genius Bar technicians with out any resolution. All of them (I really mean ALL OF THEM) said they've never heard of this issue before. The second time that I went to Apple Store, the Genius Bar technician came out to replace my phone, I asked him if he uses an iPhone 7/7plus and he said yes. So I asked him to see his phone if he has the same issue. Guess what? YES, he does have the same issue. He has AT&T and I have T-Mobile.
A couple of apple support peoples told me that it's not Apple that caused the problem because iPhone is just a device that get pushed voicemail from the carrier. They threw me to T-Mobile which I had spent several hours trying to pinpoint where the problem was. One of the apple support tole me the issue might be the SIM. I did change the SIM a couple of time. NO IT'S NOT THE ISSUE WITH CARRIERS!
As of 3/10/17, THE PROBLEM STILL EXISTS!!! Last time I talked to Apple Customer Care/Relation department was 3/10/17 and demanded for a FULL REFUND and a gentleman that I talked to REFUSED!
That was it! I stopped using the iPhone and Apple Watch S2 and now using an Android Huawei Mate 9 & Galaxy S3 Classic since then and never regret. I did sent a lengthly email (yes, I documented every calls I made with Apple) to Tim Cook and sent him on regular mail via USPS as well. Let's wait and see if Mr. Cook is just another Apple employee that doesn't care.
My business is depended on voicemail and I lost a business opportunity because I couldn't check my voicemail.
I had been using nothing but iPhones since 2007. This voicemail issue made me really angry that the original poster posted since September 2016 and now is 8 pages long and NO WORDS from Apple!
I just wanted to have a WORKING iPHONE! I miss Steve!