My problem is fixed.
I began to suspect that some setting or driver or something like Bonjour or Quicktime was not installed correctly, but uninstalling and reinstalling didn't do anything. However, I stumbled upon this: http://support.apple.com/kb/ht1925
The instructions there are much, much more detailed than on the Home Sharing help page. Uninstalation must occur in a very precise order or not everything will get removed. I went through these instructions, rebooting after uninstallation and again after installation. Voila - "Music" on the iPhone now shows the option to use my shared library. It took a long time to actually load up the library, but it's 20,000 songs so that's understandable. The important thing is that it works.
I think Apple should put better instructions on their Home Sharing help page.
Thanks for posting this. I gave it a try yesterday and it worked, kind of. Home Sharing is working fine, but Wifi Sync has stopped working when I put my computer to sleep and woke it up this morning. I've tried shutting down all Apple processes and opening iTunes again, but nothing appears.
I've yet to recieve a concrete answer on whether iTunes allows Airplay directly to the iPad or the iPad directly to iTunes, but if it is possible, I'm not getting Airplay without a third-party application.
Likewise, I've had a number of problems getting wifi sync and airplay stable. It is currently my view that you can only have one functioning correctly. Haven't got to the bottom of why and apple knowledge base only directs you to very simple debug procedures.
Firstly, I'm running iTunes on windows 7 64 bit, I have 4 airport express, 1 Apple TV, a mix of iPads and iPhones.
If you have the same setup and experience the same problems check out you event viewer and you will see the bonjour service has kicked up a number of errors. To stop this happening you have to decide what is important to you. Wifi sync or airplay?? Rubbish I know I'm sure an apple guru has an explanation but I'm yet to find anything in the knowledge base.
So, wifi sync works fine if you disable all airplay devices (no magic here, just turn them all off). Close iTunes, restart bonjour and launch iTunes again, wifi sync will start working.
If you want airplay devices stable then disable wifi sync on all your apple devices, it's a bit of pain as you will probably need to attach via the USB (as your devices are probably not syncing properly anyway!). Once disabled close iTunes, restart bonjour, start iTunes and you will see your airplay icon appear.
The key is make sure the bonjour service is running with no errors.
Hope this helps, it works for me and avoids painful reboots, iTunes installs. When I discover why this is happening I will let you all know but hopefully apple will do this before me.