OK, if Apple will release such an app... let's not start this topic. Instead, consider this example:

I've built a software that allows publishers to distribute their books on many devices at once: Kindle, iPad, iPhone, Sony Reader, etc. Do you think Apple and Amazon will allow me to release such apps for their devices? I doubt it. The only way left for me is to write it as a webapp. Such control is bad for free market in general.

  Do you think Apple and Amazon will allow me to releas
  such apps for their devices? I doubt it. The only way
  left for me is to write it as a webapp. Such control is
  bad for free market in general.

First you assume Apple won't allow such an app. Then you reason on your assumption which may have nothing to do with reality. That's exactly what I call FUD.

BTW, I bought a kindle edition of the book yesterday on Amazon.com and was reading it on my iPhone with a free kindle app. I assume, that if I had Kindle too, I'd be able to read said book on both devices. Apple did not care much where music on you iPod came from — why should they care where do books on iPhone/iPad come from? The more content available, the more useful the device is. It is hardware that makes money for Apple, and if something helps to sell more of it it is good for Apple.

I think Amazon would block it ASAP on the Kindle, actually. Their SDK license specifically states that you can't make a "generic reader".

In the reverse of these arguments, how about the DRM shenanigans around music only a few years ago? Apple was at the front of removing it.

Amazon probably not.

Apple: absolutely. There are a few such apps (based on your description) like that already :)