To make sure I got this right, this C/G is aka Inversion, right? (no second G added to the chord itself, but the G is played an octave lower). One may play the root as the bottom note or in the middle or on top.
These inversions are used often by piano players to make a chord progression more "compact". The hand does not need to jump around that much and the sounding notes are closer together, so the harmonies feel more "harmonic".
Doing this does not result in a walking bass line in any case. To achive such, a more complex way to build the "Voicing" than to focus on the compactness alone may be needed.


“Musicians”: UltraPak 2024
DAW: StudioOne Pro 6.5
"Instruments": VSTs and REs
Notation: Notion 6
Interface: NI Komplete Audio 6
Mic: RØDE NT1-A
Controller: Panorama P6/KAWAI VPC1/Atom
OS: Win 10 64 Pro