First off, punching someone ONCE doesn't do nearly as much damage as, say, exploding them with fireballs. That's why, as a MNK, you'll never see yourself doing as much damage per-hit as a similarly geared BLM. However, you hit a lot faster than they do, meaning in about the time it takes them to cast a single 1200 damage fire spell, you've hit the enemy 4 or so times for about 300-400 damage per hit, not counting crits.

As for actual logic behind punching someone as opposed to stabbing them, this is a fantasy world where you ride around on large yellow birds, fight mobile carnivorous plants, and return to the last crystal you attuned to when you die, rather than actually dying. I don't think real-world logic applies.