Are you saying you only play chords with your left hand?
And play the melody with your right hand?
Thinking about how I play, it really matters what I'm playing.
When I was playing out, I would generally play chords in my right hand, and bass lines in my left hand. (My piano teacher describes this as "keyboard style".) The melody was handled by the singer. If I was soloing, it tended to be more pianistic type solos rather than synth type solos, although I did both.
When I'm playing piano, I'm playing what's written. And that can go all over the place.
As for organ, here's an example of what you're supposed to play with your feet at the lowest level of organ playing (level 7;
RCM Organ Syllabus). A quarter note = 58. C major (illustrated), G major, D major, A major, Ab major,
And at the same tempo for in minor keys, in C minor (illustrated), G minor, D minor, A minor, and G# minor. (Don't ask why the major is Ab while the minor is G#.)
Number three is in the melodic minors of C minor (illustrated), G minor, D minor, A minor, and G sharp minor.
And that's just scales with your feet. By level 10, you're playing solos with your feet:
No, I don't know how to play organ.
Yet.
(My daughter's learning while in college. Her goal after college is to eat regularly.)