Beats is EXTREMELY WELL positioned to be a major iTunes competitor without the overhead of computer hardware and software divisions. Not only that, but while Apple is cool, Dre is much, much cooler.
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...