Thanks for doing the legwork. Any “nehhh apple BAD they make products for IDIOTS!” comment should be treated with skepticism, as usual.
Cultural cachet of Beats - note how Apple kept the brand.
Jimmy Iovine & Dr Dre showed them how to tap into a new demographic.
It helped Apple get up and running with streaming faster, they needed to compete with Spotify.
Beats brand basically disappeared after that or at the least has become "uncool".
Apple had iTunes already, they very well could've acqui-hired and improved their service themselves.
Apple music slowly died and is only becoming resurgent now, many years later.