>Unless you're worried nobody will leave a voicemail (which, I think will change over time as folks know the functionality exists),
Situation today: I get a voicemail prompt. If I leave a message it could be read anywhere immediately after I leave it or some unknown time in the future
Situation in the future: I get a voicemail prompt. If I leave a message it could be read as I record it, or some unknown time in the future
Today I'm not really inclined to leave any voicemail because it's unknown if or when it'll be read, and it's more awkward than a call or a text. I'll only leave it if there's literally no other method of communication. I don't see how having a chance that the callee will be reading the voicemail as I leave it will change this.
As it stands the main advantage of call screening is that it makes explicit that someone is on the other line. I'll admit that the advantage of being able to use follow-up prompts isn't really clear (the default prompt of "Go ahead and say your name, and why you are calling" is usually enough).