Spotify used to have this, and it's very annoying that they removed the feature about a year ago.
Note that this isn't anything particularly groundbreaking, most DJ software already supports multiple streaming services (Soundcloud, Tidal, Beatport, Beatsource, I'm probably missing a couple). This is just another integration you can choose from.
Also, Algoriddim's Djay (otherwise not a particulary important player in the market) had Apple Music support for some years now, so I'm guessing the real story here is some sort of an exclusivity contract has expired.
In most countries you need special licensing for public reproduction of copyrighted music anyway. That use case is not covered by your private streaming subscription. It´s just a means to get the media.