Hacker News Reader

There was turntable.fm. Now there's https://www.jqbx.fm which is sort of doing live DJing but with Spotify

Ah thank you. That's what I was thinking of

It was probably https://en.wikipedia.org/wiki/Turntable.fm

It's easy. Artists define a license for each track which explains whether it can be remixed.

That's not actually true within the US. Each song sample needs to be licensed individually. This becomes more complex when a song you want to remix contains samples of other songs. In general, this has become prohibitively expensive, which is why most modern songs only have a few "samples". Any company that does remixing as suggested above would have to manage the licensing in some way or pass on the risk to the users while still risking lawsuits from the music industry.