Beats streaming apparently has about 200,000 subscribers. That doesn't seem so cool when it's competitor Spotify has about 10 million subscribers.[1] Even if you think Apple is going for the subscriber base it still doesn't make sense.
I don't think it's about Apple purchasing a turnkey subscription service. Beats is an extremely strong brand with a lot of momentum who has been built from a consumer-electronics foundation, where Apple still has laptops and whatnot markets to wrangle. Beats likely does not have the infrastructure to be a turnkey rebranded acquisition anyway. However, download sales are down and going lower, so Apple does need to think about a future where streaming is dominant.
[1]:http://recode.net/2014/05/08/why-apple-is-betting-big-on-bea...