Sanest member of the asylum isn't saying much.
$3B for someone who has a streaming service just like the one you just started?
It's not "just like" the one they just started. iTunes Radio is an advertisement based streaming service and Beats is a subscription based on demand music service. The differences are monumental and the costs associated with the latter are far greater than the former. Subscription based services are sadly the future and Apple would be foolish to wait any longer than they already have to enter the game. Your misunderstanding of this fact seems to indicate that you have no idea what you're talking about...or you're willing to be dishonest about the situation.
$3B for "hot or not" fashion trendy accessory?
$400 million in profits last year would seem to indicate that the answer is "hot". The popularity of Beats headphones (whether deserved or not) by itself makes this deal a relatively safe one.
But that is a nice payday for the bankers, lawyers , and those who get to write up the hype. It isn't just this particular deal but a healthy fraction of multibillion acquisitions are busts. Whipping out this simplistic multiple isn't particularly accurate or useful for buyers. The folks brokering these deals will walk away from this deal with as much of Apple's money as they can get their hands on.
I'm willing to bet that Apple knows way more about making money than you and I do. Actually according to their profits, they know more about it that anyone in the world. Why don't we let them worry about what to do with the largest pile of cash in the world, and they can let us continue to demonstrate our wisdom here on MacRumors.