Not only is voicemail still a thing but just yesterday my iPhone took it upon itself to identify an incoming call as 'suspected spam' and route it to voicemail. I didn't tell it to do that so I guess it's part of some update Apple have pushed. I sometimes wish Apple would ask me first before that kind of thing! Although I probably would have ok'ed that one if they had asked.
Dunno about the US, but where I live (Czechia, in Europe), voicemail is simply not a thing. I've never used it in my life and I don't know anyone who's ever used it, young or old.
We have it here for mobile but by default providers set it to "call waiting" instead. One of the reasons people don't use voicemail (other than not knowing it exists) is they charge you money to leave a message. Your plan minutes don't count. They probably charge you to listen to messages too.