It doesn't take a genius to figure out why iTunes is anti-web: iTunes was originally released in January 2001. The best-of-class web browser at the time was IE 5.5. IE6 was nine months in the future. Safari was two years in the future. Firefox 1.0 was nearly four years in the future. The XMLHttpRequest object had not been invented. The term "Ajax" was four years in the future, as was the first famous Ajax application, Google Maps.
Apple is a farsighted company, but surely it's a bit much to expect them to have traveled half a decade into the future and brought back Web standards that didn't exist yet. And, let me assure you: Web versions of iTunes built with the technologies of January 2001 were terrible (cough Java applets cough) compared to iTunes. That's not a hypothetical -- lots of people built such apps. They're all forgotten now.
Why, now that things have moved on, doesn't Apple abandon the iTunes model and build a web app?
A) Because iTunes needs to connect to iPods. Can you build a web app that can reach out over the USB ports and talk to an iPod? I'm pretty sure that, if I could, it would be treated as a dire emergency and high-priority patches would be issued. If I can talk to your iPod via JS, I can talk to your hard drives.
Even the Amazon music store communicates with iPods via... iTunes! There are few other ways, and no other sanctioned way.
You could, I suppose, reduce iTunes to a tiny browser plugin or a stub, but that would still require users to download and install a third-party plugin, and it would lead to problem B:
B) Now that iTunes is established with millions of existing iPod owners -- who are Apple's best customers, now that so much of iPod sales are to people replacing existing iPods -- why make a major change in their workflow, with no benefit for them and trivial benefit for the world? The risk of confusing one existing iPod customer may well offset the potential benefit of getting several new music-only customers like Jeff -- who obviously doesn't own an iPod or he wouldn't be complaining.
Plus: Cross-browser maintenance of an app as complex as iTunes is expensive and difficult, you can't control every aspect of the UI, and the population of people who balk at iTunes is small and is unlikely to contain many loyal Apple customers.