This chord is extremely common in modern musical theater, to the point that I sometimes call it "the musical theater chord". I've also had a lot of arguments about how to properly analyze it.
I've run into a lot of people who absolutely insist on calling it G9sus4. With G in the bass it's natural to call it some kind of G chord, but I think "9sus4" does a poor job of explaining the other notes. In particular, it doesn't explain the lack of a D. This D isn't omitted because of voicing issues (the way it is in a #11 chord, for example) or because we've run out of fingers, it's explicitly missing when it could easily be present, and that's a tough thing to account for in the analysis. Furthermore, accounting for the C as a suspended 4th has several problems:
- The lack of a D weakens the sound of a suspension
- It's often doubled (on piano, the right hand often has C-F-A-C), which is terrible voice leading for a suspension.
- It never resolves to a B, and instead the voices on C stay on C as the chord resolves.
I think this analysis has too many holes to hold water. Calling it an 11th chord at least avoids these problems with the C, but still doesn't account for the missing D or explain the very particular voicing in the treble.
Calling it an F chord happily explains all of the treble notes, but that G in the bass is hard to explain. It would be Fadd9, with that 9 in the bass and explicitly not present in the treble, which is a flimsy analysis.
Whenever there's a chord that's ambiguous to analyze, I use a tool that I call the "simplification test". If you hypothesize that a chord is a G[insert crazy extensions], then a plain G chord (or maybe the appropriate 7th chord) should function the same in its place and merely have less color. At least in the musical theater context, the chord that most strongly passes this test is F. I agree completely with your idea of it being a plagal cadence, with a little bit of authentic motion in the bass to strengthen it (and also add a bit of tension to be resolved).
Chord symbols in sheet music have two main purposes:
- To explain the theory
- To provide instructions to a musician and get them to play the notes you want
The theory debate may rage on, but I hope everyone can agree that as a practical instruction to players, F/G is the label that will cause people to play the intended notes. A guitarist will see this and play an F chord, a bassist will play a G, and a pianist will play F-A-C in the right and G octaves in the left, and that's exactly what we want. G11 or G9sus are both going to cause most people to play Gs and/or Ds in the treble.