Why would you want to export the data? to save voicemails?
Of course, there's a difference between why you would want to export your data and why you would want the ability to export your data.
That wasn't actually my question here, though. My comment is actually about accessing it--why not just go directly to the service to access the voicemail?
The Data Liberation Front seems to be trying to untie your data from the services that use it, because it's yours and can still be valuable to you after you've stopped using said service.
Yeah as well as text messages, phone numbers (for importation into other contact systems) etc. backed-up and archived for work/business (even personal) purposes.