Good Morning Alec,
Your next to last post in which you discuss the Csus2 chord forced me to put my thinking cap on and do some reaearch, hence my delay in responding. Please understand I am not being argumentative or disputing your harmonic logic. I'm merely trying to contribute positively, and hopefully constructively, to this thread which began with KN6Guy's question regarding the C2 chord he was playing.
I have searched my two books on harmony and nowhere is a Csus2 chord mentioned, let alone discussed. I have a book entitled "7,488 Keyboard Chords", another entitled "The Complete Encyclopedia of Chords", and still another, "The Definitive Chord Book for Jazz and Popular Organ", and none mention a Csus2 chord. It is certainly not a commonly used chord in harmony and it is possible it is a misnomer.
This will be a bit long-winded and I apologize to our readers for that, but there is no other way to say what I believe to be the case regarding the so-called Csus2 chord.
It is true in harmony that ANY note can be suspended (sustained) from one chord to the next chord without breaking the rules of harmony. However, the word "suspension" implies something left hanging that needs to be resolved (released). It is a note that creates tension.
In your example of a Csus2 chord you cite the notes G,D, and E. When determining whether a chord is a suspension or not, one must first look for a root note. All suspended chords include the root note of the chord name. In the case of your Csus2, there is no C note, therefore it is unlikely those notes comprise a Csus2 chord. I believe those notes are in fact the notes of an E minor chord. In your example of a C7sus4 chord, the root note C is played, hence it is a legitimate suspension of a C chord - in this case a C7sus4 chord.
You remarked, "The C2 is surely a suspended chord." I concede the "sound" of the notes G,D, and E, when played, create the same sound effect (tension) as a suspended chord when played in isolation, i.e., without reference to any other chord in a progression. The problem lies in naming the notes G,D, and E as a Csus2 chord. Let us consider for a moment the Csus4 chord and its notes C,F, and G. The rules of harmony dictate that to be a legitimate suspended chord, the suspended note must resolve within the chord being played, not upon a new chord. Therefore, in the case of a Csus4 chord, a C chord is being played and the F is resolved to E.
In the case of your Csus2 chord (notes G,D, and E), each note forms the root note of a chord and none of the chords formed use the note C. That is why I suspect the Csus2 designation is a misnomer and the notes are in fact part of a legitimate chord - in this case, I believe, an Eminor or Eminor7. When you play G,D, and E (Eminor), then play the note C, you are changing chords (moving from Eminor to C major). Thus the three notes cannot be a Csus2 chord by rule and definition.
I don't know if this discussion sheds any more light on the subject or not, and again I say, if anyone can add more to what has been said already, please do. I love to learn.
We have a beautiful sunny day here in the U.K. and the thought of being on a golf course is overwhelming, so that is where I am headed. I hope everyone has a sunny day.
Best Regards to All, Chuck