Can't you just dial your own phone number to reach your voicemail?
Back in the Blackberry days, digital and data on your phone was kind of a new thing. I bet their way of logging into your cellular voicemail was based on the analog system, kind of based on how land line voicemail worked before everyone had cell phones. They probably just figured out a cheaper, more efficient way of connecting you to the voicemail system, rather than dialing a phone number. Once all the phones were switched to this magical new system that I'm completely making up based on my assumptions of how things work, they killed all the phone numbers since you weren't supposed to be using them like that in the first place.
http://paysimple.com/blog/2012/01/30/how-to-leave-a-voicemail-message-without-ringing-the-phone/You dial 267-759-3425, put in the number you want to reach and then listen to an advertisement and it connects you to the voicemail. I've never tried it myself, so hopefully it still works.