iTunes feels like more of a dinosaur than AOL did by the early 2000s. AOL at least tried to keep up with the times for a while.
Apple's problem with services is rooted in the way they approach products in general. It takes Apple an enormous amount of time and resources to come out with a product. When they finally come out with it, it's well-polished. But it never really changes after that. Apple lets the product waste away, and eventually it's supplanted by something else. With iTunes you can see that Apple has tried to make updates, but those updates have turned iTunes into a mess, and the core iTunes Store experience hasn't changed. I would say it's gotten worse. Searching is incredibly unwieldy across apps, books, and music, and can't compete with the convenience of streaming unlimited content. Apple has never gotten Internet services. They've shuttered all the online services they've ever created except for iTunes. They didn't improve .Mac; they shut it down. They didn't improve MobileMe; they shut it down. They had to send out OS update discs just to get people to migrate their e-mail to iCloud. Who else has an e-mail service that is reliant on a particular OS?
It seems like iTunes is a chore to them and has been barely kept alive in order to remain compatible with all the devices they sell. If Windows is Microsoft's legacy product it has to maintain for past compatibility, Apple's equivalent is iTunes. But the original iTunes and original iTunes Store were both amazing. It just seems that Apple can't do things well until they scrap something and start over.