Fine, not everyone. But there will be an impact, and it is likely to be significant. For some, not all, it could be disastrous. It doesn't mean the end of indie music and indie labels, but it's still enough reason to be angry.
The music belongs to the artists that performed and wrote it, and to the labels that paid for it to be made (often one and the same). It isn't Apple's to give away for free, in the same way I'd never let anyone else use my licence code for Logic Studio.
A limited time free trial isn't the same as giving your product away for free. By your example, lots of expensive major software is provided with a free trial period. It doesn't destroy their business - on the contrary those that like the product pay for it, and those that don't go elsewhere.
Might there be an impact? It's possible, but I can't imagine it would be anything catastrophic like you are making out. What happens when any new streaming service launches and offers a free trial? Is it horrible and business-ending? You are basically assuming that in one concerted action, the iOS user base is going to update to iOS 8.4 (required for Apple Music) and immediately start the free trial, immediately stop everything else. There's just no way. What we will likely see is a staggered base of people upgrading and trying Apple Music. Many may not update their phones until the Fall and not start their trial till then.