Disclaimer: I work for a cellphone operator.
Ok, TFA has some valid points on the endless annoyance that we know as voicemail. But for mobile operators, at least, there's really no reason for them to kill this service.
And do you know why? Voicemail is considered, from a telco point of view, as a Call Completion Service. This allows the operator to generate revenue by forwarding a call that was destined for termination (B-party hung up, rejected etc) into a service that answers the call. At which point, they can charge the caller for this "previlege".
Let's say operator X has 100 million calls per month on its network where the called party has rejected the call or is unavailable. Assuming that:
* a chargeable block of 0.10 per minute
* everyone leaves a short message that's less than one minute long
The operator stands to make $10,000,000 a month in call completion revenue. By providing a simple voicemail service. Which no-one really cares about anyways. Of course, there'd be interconnect charges from other operators, but the gist is the same.
If voicemail was removed, the operator would lose this significant chunk of revenue, just because there was nothing to complete the calls. Which is why you'll never get existing operators who already provide voicemail removing it.
Voicemail == Call Completion == Cash Cow
Where I'm working, revenue from this call completion bit contributes around 20% of the monthly voice traffic revenue.
Another fun factoid: voicemail retrieval stands at 10% of those deposited.