Basically, you are looking at it as if every chord is also an inversion of another. Technically they are, but they don't sound like it.
A G/C will sound like a G chord with a C in the bass, same as if you do a powerchord but throw in another 5th below it rather than the lowest note being the root, sure, technically its a Sus4 chord, but does it actually sound like that?
You are best thinking of chords in their lowest common denominator, in terms of rather than thinking of, lets say Am/G, with the notes GACE, in G you would be looking at a G6add9 minus the third, but if the song you are playing is in A minor, it will just sound like A minor with a G in the bass, hence its just an Am/G