There's actually a fairly simple answer to that question: we don't care. Seriously, we care not a jot nor tittle, nor anything earthier and more Anglo Saxon, about the survival or not of the music business in this digital age. Just as if we're thinking straight we don't care at all about the health of any business ever.
For we don't in fact care about the profits of business, the health of business. We care only about the ability of consumers to consume.
Now it's undoubtedly true that digital copying, the internet, bit torrents etc have reduced the ability of the record companies (and to whatever extent they ever got any of it, the musicians) to monetise their products. But that's not what we actually care about, what we want to know is whether we the consumers have been able to consume more music as a result. Which clearly we have.
We need to go a little deeper though. Such things as copyright protection are not there to aid producers: they're to aid consumers again. For we recognise that a limited property right in new creations encourages such new creations. Thus, such property rights increase the number of new creations that can be consumed. And yes, that really is the reason why we have the whole structure of intellectual property. Nothing at all to do with just rewards, all entirely to do with incentives to allow consumption.
So what we'd really like to know is whether there has been a decrease in new composition in recent years, perhaps even a reduction in the quality of those new compositions, as a result of digital copying. It's a slightly difficult thing to test that as by definition any music written after the listener passed 21 is rubbish to said listener and anything published after they're 30 is simply noise. That's actually one of the points of pop music, to differentiate between the young and the old.
However, using a set of techniques, each independent but each of which provide roughly the same answer, Joel Waldfogel  has been able to show that there has not been a decline in quality since Napster spearheaded the don't pay a red penny for music thing.
The answer is, as he says, that while monetisation of what is created has become more difficult, the very same digital revolution has lowered the cost of creation. Given that the incentive to create is not the income from having done so, but the net income, the incentives to create still work.
Thus, given that what we actually care about is consumption ability, we don't have to worry overmuch about the business models of the music recorders and distributors. At least not at present. For we're getting to consume a similar amount of high quality new creations but paying less for being able to do so.
That is, the consumers are getting better off and as for the producers, well, we only care about them to the extent that consumers are getting better off. Or as in this case, we don't care about them at all.