Some exciting news:
With the help of a tester (thanks kyeh!), #mobilelinux though vvmd/vvmplayer ( https://gitlab.com/kop316/vvmplayer ) finally supports Visual Voicemail on all major US carriers!
If you have an MVNO on any of the major carrier, you should be able to easily check if the parent settings work for you. If they do, *please* make an MR in https://gitlab.gnome.org/GNOME/mobile-broadband-provider-info so we can officially support more carriers!