One disadvantage is that your phone would need to be turned on and in range to receive the message. This could be solved by a hybrid system where the carrier al

One disadvantage is that your phone would need to be turned on and in range to receive the message. This could be solved by a hybrid system where the carrier also stores it. A perhaps more important factor is that when you call the carrier to get your voicemail, you sort of automatically know you'll have to pay for it. But if your phone silently downloads a message you may never check, not so much. So that crestes a billing problem.