A few reasons I think. First, it would step on the monk's toes if anyone could do a lot of damage with a fist or kick. Second, fists and kicks just plain don't do much damage unless you are trained in a martial art. I suppose they could make a feat or fighting style that would represent a martial art and raise base unarmed damage, but simply being a fighter or barbarian shouldn't do it.
I agree, unarmed combat requires extensive training, including medical knowledge about the anatomy applied practically. Without knowledge, the human natural weapons are typically nonlethal.
I disagree about the Fighter class stepping on the "niche" of the Monk class.
Unarmed combat is probably even a biological instinct among humans. If there is anything that every class should have access to is learning how to fight effectively without implemental weapons. How would every class know how to use shortswords and shortbows yet somehow not be allowed to fight unarmed effectively?
Moreover, the Fighter class can specialize in ANY weapon. Conceptually this includes the use of ones body as weapon. If anything, it is the Monk that steps on the niche of the Fighter.
Moreover, when the Fighter class engages body-weaponry, it does so from a strictly nonmagical perspective − in the sense of a purely martial power source. By contrast the concept of the Monk class is magical. Whether the class is by definition using the psionic power source, it is in any case using the more mystical aspects of one own "soul" − as psionic does as well.
It is the mystical aspects of the Monk concept that allow it to substitute Wisdom and Dexterity instead of the benefits of Strength and Athletics. A Fighter approach to bodyweapons would orient similarly on highly-trained high damage unarmed stikes, but do so from the perspective of Athletics and grappling. Again with high damage. Typically, a Fighter should be doing d8 damage per strike. If there is plot protection, the base damage might be 1d6, but with bonus damage coming in from other resources.
The Fighter concept deserves to fight effectively unarmed − as one of the many choices of weaponry in the arsenal of the class.