While thematically awesome, having a natural attack as a favored weapon is rather pointless because a cleric / inquisitor / warpriest gains free proficiency with their deity's favored weapon. So if a natural attack is your favored weapon, you gain free proficiency with that natural attack ... except it actually does nothing. Even if you're proficient with, say, a bite attack, you can't attack with a natural attack that you physically don't possess, just as you can't attack with a longsword you aren't wielding even if its your deity's favored weapon.
Likewise, any creature that gains a natural attack is automatically proficient with it as per the natural attack rules in the Bestiaries. This is why the Draconic Bloodline's 1st-level power doesn't need to call out that the sorcerer is proficient with his new claw attacks. So ultimately, you get nothing.
Now, granted, there are some feats that require you to have Weapon Focus with your deity's favored weapon and with the new warpriest class, a warpriest of Aspu can use his bite attack (if he possesses one) as his sacred weapon. But in most cases, you don't see it often because it sort of gips clerics out of a class feature. (See Aspu and Dahak above, who both offer two favored weapons for this very reason.)
It's pretty neat for Crusader's Flurry.