Block chord and barry harris chord style playing is a post 50's thing and is very much two handed. All organ and many piano players can do left hand bass lines while playing if they have no chord playing. The fact that the melody is typically above the chords is an arrangement thing based on acoustics and psychoacoustics (look up masking). You can't just do the same thing anywhere on the piano without getting muddy sounding, so unless you want to cross your arms...
Most pianists put the melody on top because it sounds better and doesn't conflict with the bass.
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Block chord and barry harris chord style playing is a post 50's thing and is very much two handed. All organ and many piano players can do left hand bass lines while playing if they have no chord playing. The fact that the melody is typically above the chords is an arrangement thing based on acoustics and psychoacoustics (look up masking). You can't just do the same thing anywhere on the piano without getting muddy sounding, so unless you want to cross your arms...
Most pianists put the melody on top because it sounds better and doesn't conflict with the bass.