I predict Apple will introduce an iTunes client for Android soon; it probably just opted to wait until after Google dumped a bunch of resources into Google Music… Perhaps the Android iTunes client will also be buggy and run hot, e.g., like the Windows PC iTunes client.
Instead, real people will make a simple non-decision: If they use an Android phone, they can’t use Apple’s store or locker. So now they can use Google’s. And while it will be theoretically possible for iPhone users to use Google’s store and locker, it will involve some kludgy sidesteps that won’t appeal to mainstream users.
And that’s about it. In the end, this isn’t about helping Google “catch up to iTunes” — it’s about filling the big, gaping, musical hole in Google’s mobile business. But as market report after market report has pointed out, the lack of a music store — and a decent music player, for that matter — hasn’t hurt Android sales.