One of the best and quick fix to this issue is to turn off Wi-Fi for once and switch to Cellular data connection and then try to change the default greeting to custom on iPhone.
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With notifications, you're alerted when you miss a call or receive a voice mail message. You can decide how and when you want to be alerted. For example, you can receive an email when you miss a call or get a text message when someone leaves a voice mail. By default, you'll receive an email anytime you miss a call, but text messaging notifications are turned off.
Voicemails don’t necessarily have to be monotonous or extremely jazzy or funky. What you should be looking for is a balance between the two. Whenever you call someone and their voicemail greeting is playing, it tells you a lot about who they are, as a person. Which is why, you’ve got to put a little bit of “you” when it comes to voicemail.