I think there's a bit of a muddle on this thread - we've had the capability to do text-to-speech on computers for many years, I remember my 80s IBM PC being able to gabble in a very robotic computer voice, and for some years now a computer has been able to read a human-written script almost naturally.
What's changed in recent months is the ability for the computer to write the script in a variety of styles and registers. It can take various sources of information - music trivia, local events, weather, traffic - and write a presenter link, and then read that presenter link. It can react without human intervention to changes in circumstances - developing news from a news feed, a crash on a bridge from the Inrix API - and update what it's saying in real time.
Having said that, I've been unimpressed with the demos of Spotify's DJ that I've seen so far - it seems to be limited in what it says and keeps coming out with things like "so you've been listening to lots of 1990s dance music lately, here's some more 1990s dance". Hardly award-winning personality radio. I can see AI eventually developing to the point where it's replacing jockless hours on small-market stations, but radio's USP is the connection with the human personality, and AI can't do that just yet.