This wouldn't make much of an impact because the statistical distribution of music listening time has an extremely long tail, i.e. the most popular songs are far more popular than even other very popular songs. In a given market, something like 90% of listening time will come from the top few hundred tracks, and 99% will come from the first couple thousand. Those top couple thousands tracks are already well-served by alternative distribution channels (youtube, "indie" labels, etc), so there isn't much room for disruption there. Starting a service to fight for that 1% of listening time will not move the needle.
source: I used to work in the data side of the music industry.
Rather, Bandcamp should start a streaming service. I've had a payment model in my pocket for years that I think would work really well for them.