God, no.
This feat is insanely powerful. Anyone who DIDN'T take it at level one would be a fool. A class with a one-to-one attack bonus can double it with this feat; a class with a one-for-two attack bonus triples theirs.
While the restriction on one particular non-magical weapon may seem to balance this, unless you make a habit of sundering weapons every session, it doesn't cut it. Especially if, as someone else pointed out, a monk takes this feat for his unarmed strike.
Finally, this feat makes Power Attack or [Superior] Expertise another must-have feat, as you will always have attack bonus to burn for extra damage or AC. Consider the 20th level monk with no extra attack bonuses aside from this feat. He will attack for +35/+32/+29/+26/+23, for 5d20 points of damage. If he chooses to Power Attack for maximum damage, it becomes 5d20+45, with at least a good chance of hitting with every attack. Maximizing AC with Superior Expertise would mean an stacking AC bonus of 15, which pretty well makes him unhittable, especially with a good Dexterity and/or Wisdom.
In other words, this feat is extremely broken. No way would I allow this thing anywhere near my games, as a DM or as a player.