I have an iPhone 4s on AT&T. I'm going to want to switch to an iPhone SE and also switch to Cricket Wireless. Cricket shows on their website that you can have 20 voicemails, but they also have a page giving instructions to set up Visual Voicemail in iOS.
On AT&T right now, I don't have to manage the voicemails. It appears that iOS downloads the voicemail from AT&T and deletes it from their servers. It's good because I never hit a limit to how much voicemail I can save and never have to manage or delete anything.
Does the same thing work on other carriers, like Cricket, being managed by iOS directly, or does it vary by carrier?