Your model is basically saying that since the artists already did the work, "they're not losing any money or time" if somebody else gives away their music for free.
Yes, you can say that. After all, why should you ever pay any artist? They already did the work, so they aren't losing any money, right? People are merely using their work for free without paying.
Here's the problem: "recognition" doesn't pay bills. It's nice, it's flattering, it's great for the ego, and the net result is you starve. Apple's business model is that artists should be happy that Apple had decided to give their music away for free in order to promote Apple's new business, and they seem surprised that artists actually would prefer to be paid.
Here's a tip for you, for future reference in case it ever happens to you: when you're being told "you work for free, and maybe sometime later I'll pay you", no matter how good it sounds, the deal is always going to be to the advantage of the corporation getting the free work, and not necessarily for you.
Well, Apple backed down, at least a little. Good for them. Horray for Taylor Swift.