I love that these type of apps are popping back up. However, I fear that the RIAA is going to ruin all the fun like they've done in the past. I used to run a site in which we just played random music with no ads/no revenue. We still got a cease and desist letter giving us no choice but to shut it down. I get why they exist, but they are more about stomping out sites rather than working them to figure out a path that is lucrative for everyone involved.
Unfortunately the only way to get around this is to have agreements in place with independent artists for the site that you could then provide to the RIAA when they come knocking. If you post music by artists signed to a label it's out of the artists' hand even if you attempt to put something in place directly with the artist. The RIAA is aggressive and well funded. Their entire objective is to make sure artists get paid whenever their music is played regardless of whether the site is free/no ads.
EDIT: Spotify, Apple Music, Pandora, etc do not provide APIs to embed their players into other sites without some sort of licensing agreement in place.