Maybe not the most ideal privacy choice, but you can also setup conditional call forwarding so that voicemails get redirected to another service such as Google Voice, YouMail, etc. Google Voice does Visual voicemail and it's very convenient to have voicemails backed up rather than having to figure out how to move them whenever I change phones or SIM cards.
If anyone knows of a privacy respecting alternative, please chime in. I've been using Google Voice both for voicemail and as a backup line for 2FA codes where I'm forced to use SMS. It works really well, but one less google spp in my life is usually a good thing.