It would be great partially because the existing sync solutions for Android are all a little bit wonky. I don't think it would necessarily be great for Apple, though - I'm considering purchasing an iPod to listen to music on to get that better integration, and releasing iTunes for Android would commoditize the listening device - exactly what a shiny hardware manufacturer does not want.
Winamp was OK but crashed a little too often for me to be able to rely on it. DoubleTwist is, hands down, the worst music software I have installed on my laptop in recent memory (I can expand on this if you want, but my overall summary is: terrible). I hadn't tried WMP or Android Cloud Player, and at the time Google Music wasn't available to me. Spotify I haven't tried yet because until today, I couldn't even get it to see my phone despite my laptop and phone being on the same wireless network, as per the instructions. It has finally shown up though so I will give that a go.
iTunes supporting Android would be great for all Android users. iTunes is a great market with excellent apps which are not ported for Android.Unfortunately,like you said,Google will never allow this.
I was thinking more for a music point of view. How many users could Apple win over into the ecosystem just by letting you sync your iTunes library with your Android phone? I'm thinking a lot.
I'm sure that, to Apple, the more relevant question is: How many iOS device users would they lose by letting you sync iTunes library with your Android phone?
I'd guess a lot, but even if that's wrong, it takes hundreds of incremental music sales to offset the loss of just one iPhone sale.