Spreading a chord over two hands isn't really using your left hand though.... and playing random shell chords isn't really either. Playing an actual walking bass, stride, four-to-the-bar chords, arpeggios or boogie patterns is more like it.

> Spreading a chord over two hands isn't really using your left hand though

Kind of like how running with both legs isn't really using your left leg? I don't really understand this train of thought.

> playing random shell chords

Not many piano players these days use bebop era shell chords. It's all about rootless, cluster and quartal voicings. And just because they are played without regularity doesn't make them random. A skilled player places them very intentionally.

> Playing an actual walking bass, stride, four-to-the-bar chords, arpeggios or boogie patterns is more like it.

These techniques create a metrical regularity that is antithetical to the spontaneous and forward-pushing rhythym of post-bop era jazz. It's fine for certain styles of music.

Also most of those don’t work too well in a group setting, where other instruments are already serving the same purpose.