@Ian Davis
Yes, iTunes came out before the iPod. And what a massive fricking success it was!
...oh, wait. It wasn't. To a rough approximation, no-one used it.
Notice I said Apple had an artifically created monopoly in SOFTWARE music players. Their monopoly in hardware music players is not artificially created - people buy iPods qua iPods, either because they think they're really good, or just because they're popular. That's fine, Apple doesn't do much to artificially maintain that monopoly.
The same is not true of software music players. Most people use iTunes not because they chose it over other music software based on its (real or imagined) merits, but because they have to use it to talk to their iPod. Note, again, the important point that Apple doesn't just actively work to stop iTunes working with other hardware players - they actively work to stop the iPod working with other software music players. If you buy an iPod (or iPhone), you're locked into iTunes.
Because Apple has parlayed its hardware player dominance into software player dominance, we're left with a dysfunctional music player 'marketplace' (on Windows and Mac) which results in large numbers of people being forced to use iTunes, not because they particularly like it, but because Apple makes sure nothing else will work with their iPod. Hence anyone trying to compete with iTunes is stuck on an unfair playing field - they can't make their application sync directly with an iPod or iPhone, so it's more or less doomed to niche status.
Yes, other apps can talk to iTunes via an interface it provides, but the whole point is that's nothing like parity with iTunes. It's the poor man's option. When iTunes is obligatory (you can't talk to the iPod directly, you can only talk to iTunes) but the other software is optional, which one looks like a pain in the ass to the user? Hint: it's not iTunes (although if people stopped to think about it, it should be). As I said, no-one thinks of the Blackberry as a top-tier music device, do they?
Finally, please stop trying to pretend there's some incredibly special secret sauce to the extremely simple business of synchronizing a music library with a hardware player. It's ridiculously simple. Again, look at a non-dysfunctional system to see how it should work. Rhythmbox, Amarok or Banshee on Linux can all synchronize a music library with just about any portable player (even some iPods, where Apple hasn't yet successfully managed to lock them out), as seamlessly as iTunes works with iPods. It's really not that fricking difficult. Most music players are just mass storage devices anyway. Many that aren't use MTP, which is a decent protocol with a good common Linux implementation (libmtp). For the oddballs like the iPod that don't, other libraries have been written. Then there's a trivial bit of HAL which identifies devices as music players (based on their USB IDs) and defines what formats they can support and what directory the music files have to go in. Then the players have simple code that converts files to the appropriate format (as provided by HAL) and copies them onto the appropriate place on the device, either directly for mass storage devices or using the appropriate helper library for MTP devices or oddballs, and updates the player's database if appropriate (helper libraries do this too). It's really bloody simple, and it works great with any player whose manufacturer isn't actively trying to lock third-party software out of their devices.
This is how it ought to be on Windows and OS X, but because of Apple's artifically-created software player monopoly, it isn't. That's the problem here.