ARFOR
It is evident that your knowledge of US NAS is limited by Internet Explorer.
It is a great shame that you cannot speak with any authority as one that has flown in or provided ATS services under US NAS.
Your cut and paste exercise only proves that IFR pickup is available as we have been saying.
You really will cut and paste anything that appears to cast doubt on anything that a NAStronaut states. (thanks for coining that phrase... I am indeed a NAStronaut)
You really should read what you post more carefully. Your ATS manual excerpt of section 4-3-9 assumes that a pilot requests a VFR departure.
What your Internet Explorer did not tell you is that there is absolutely no requirement for a pilot to request a VFR departure. They can just do it!
Of all the VFR departures I have conducted in the United States, not once have I asked to do it and not once has a controller had to 'authorise' it.
Why don't you go and ask one of your American colleagues how its done in the United States ARFOR, I hear them on the radio here every day. I'm sure they will explain it to you, they seem quite friendly.