So far the closest thing I found was when Huey Lewis did a radio show on Apple Music. You couldn't call in and there were no contests, but it's a bit of talking from someone likable, separated by a couple of songs they introduce which you also like. That's basically the format of radio, in its most basic form.
I've searched a bit for that type of format on streaming. Sure there's always TuneIn or MyTuner apps which are interesting but those shows are always tailored to a specific faraway city that you don't know much about, or they're in a different language, or they're sports talk related which I'm not interested in.
I'm specifically looking for music I like and a likeable person talking and introducing songs, just like the clips you have on your web site. I just don't understand how that can be so expensive that big tech companies with deep pockets like Apple Music don't want to produce it. What's up with that?