I've never read proprioception described as a sense of balance before. AFAIU, proprioception is the sense of where your body parts are in relation to each other--arms, legs, head, eyes (and eye gaze), and much more that's difficult to enumerate or describe. I guess that's critical to maintaining balance, but not sufficient? Summarizing proprioception as balance seems wrong even if the inner ear vestibular system (which is where our "sense" of balance is regulated, AFAIU) is a component of proprioception.

And in addition to proprioception, we can sense hunger, thirst, tiredness, time, temperature, balance, our own movements, pain, pressure, and maybe even itching. It's just that "we have discovered a seventeenth sense" has less glamour to it