Well, I must be unnatural then, as I do sometimes sing and accompany myself on the B/C. As for aesthetic reasons, yes, the box is pretty loud and in a session it would be very easy to drown your singing out by playing too loudly. So I would tend to just play a few chords and let the voice supply the melody while singing the verses, and then bring the right hand in for any choruses or instrumental breaks. My favourite keys for singing, depending on the range and register of the song are D, G or A, all of which work fine with a B/C.