Ok, I give. The Touch clearly doesn't meet your definition of a PDA. You win. I guess my point is that not everyone subscribes to your definition. The Touch is clearly not as capable as some other devices in many areas. It works great for me, but I'm not a 'power user' like you seem to be. It's clear that you feel very strongly about this, and I respect your opinion.
Specifically regarding Air Sharing, it sounds like you have a misconception about how it works. Think of it as a viewable storage device. While the Touch (or iPhone) is a client on a network it is an addressable storage device -- on your computer it looks just like any network drive (public/private access is controllable with password protection) and you can access its contents in a Finder (Mac) or Explorer (PC) window. You move files to and from the Touch by dragging and dropping and the files
are loaded on the Touch itself. The files aren't hosted anywhere. You're right, you can only do this from the computer end, just as you would access any network drive from a computer, not the drive itself.
Once the Touch is off the network (when you're on the go) viewable files are available on the Touch itself, without being dependent on any other storage devices or connections to them (supported file types
here). You can't initiate movement of the files to other devices from the Touch's interface, but if you connect to another network the files are again accessible to other devices on that network.
Hope that makes it more clear. My guess is that it doesn't do everything you think it should, but that's what it does do. Works nicely for me. I load files onto my Touch at home, and then can view them wherever I am (no data connection required). I can also share them if I want to by connecting to another network.