That is something that would be of interest to those working with splitting audio into 'stems', drums, bass, voice, music. Algorithm DJay can do a version of that 'on the fly'. Serato Studio is a kind of remix 'on the fly', but there are many others. Both have automix settings that work very well, especially if you line up similarly grouped tracks.
Yeah, I've not used the "auto" features to that extent, but I've DJ'ed at a few events and festivals just for fun and it's super convenient to have software that has analyzed my music library for BPM and key. I still get to play whatever I want to play, but if I'm drawing a blank or just looking for inspiration, I can sort by all tracks within "n" BPM of the current track and in the same/compatible key.
Then if I really want to play something that wouldn't normally fit with an easy transition, I can always adjust they key or tempo on the fly. There are limits before it starts to sound weird, but that can also be a neat way to mess with a song. Add a riff or a phrase from one song into the current one, but only because I'm able to halve the speed or chop up the time signature to match.
And that's just me as a barely fluent hobbyist. Experienced DJs can do some great stuff. Even a non-"mixing" DJ like a radio DJ can string together songs based on thematic connections, sneaky relations between artist or lyric or even the conditions in the room. Those can be a lot of fun and would be a lot harder to automate than simple beat matching.
