"But I would like to see some specifics on how these freedoms would be used, so that we can discuss the real advantages they would deliver and weight them against the real security holes they would create."
Will try to provide some.

Allow applications to be installed at the user’s discretion, not Apple’s ---
Why would we recreate the wheel ? Let's just look at what other operating systems do : an apt-like system would be perfect. You would have official sources list for downloading secured apps, and the possibility to add custom sources.
I can't understand why some seems to disagree with this request. If you want a secure iPhone/iTouch, then just don't install untrusted apps, but don't blame the others. On my N70, i needed some apps and i created them for a personnal use, I'm puzzled not to be allowed to do so on my iTouch... it's mine, I paid for it, why can't I install what I wish on it ?
Why does Apple think they are more able than me to determine wether a program is dangerous or not ? Especially if i wrote the program myself.

Allow applications to run in background on iPhone ---
This is absolute necessity!
Very often, you have to look for something while you're doing something else :
.Writing an sms and want to switch to contact list to remember the birthday of a friend.
.Listening music while watching pictures.
.Looking for a map on internet while writing a message to explain to a friend how to go somewhere.
.Resume the text you were reading while an sms/alarm emerged.
...

A MediaPicker API for accessing the iPod music files is needed --- Necessary too !
This would transfer the handling of media formats from the OS world to user world. What if I want to listen .xyz files, the new "a la mode" music file format ? What if Apple just can't pay engineers to constantly update their viewers/players to be able to handle latests formats ?

Each request I illustrated here is not in contradiction with the "non-Mac" mantra. They are just necessary...
The other requests are more tendencious: Allowing developpers to access ports might lead to completely unstopable apps aiming at replacing Apple softwares.
Allowing a root access or a filesystem access would just break the abstraction layer provided by the SDK -> Mac OS Mobile is a monolithic kernel (euphemism), user-land softwares are highly abstracted. But adding a shared file-storage location would just be perfect.

Excuse me for my poor english :-)