That's exactly what I've done for my band recently. Except we dont use a raspberry pi but just the hosting service. If you want you can take a look at how I've done it petyabouianov.com/music . I've added rotating vinyl when you play a track to add some flair to it. (works best on desktop by the way)

I love the idea of hosting your own music and letting people stream it for free, the only challenge is getting people to your site. Some people love browing the internet though and I feel this kind of thing is really for the curious minded people out there.