Well, I concur with shilson. To make the feat moderately useful, it needs to allow two extra smites per day. At that point, it becomes a balanced feat. A fifteenth level Paladin only has 6 feats (seven if human). There are any number of general purpose combat feats that will end up being more useful (Improved Critical, Combat Reflexes, Improved Initiative, Close Quarters Combat, etc.) and that isn't even getting into the fact that many Paladins are going to want to take mounted combat feats for flavor and to make the most of thier mount. The chance to spend a feat to get one extra attack doing 15 or so damage just doesn't seem worth it.
Suppose a 15th level Paladin gave up all his feats to Smite 15 times per day; it would not bother me in the slightest as a DM. OK, he is a potent one trick wonder, but I tend to throw a mix of creatures against my players - and he has nothing up his sleave vs. oozes, constructs, gargantuan vermin, dire animals, plants, many if not most beasts and magical beasts, a good percentage of the humanoids and elementals, and a fair percentage of giants and aberrations. OK, so he can do +15 damage for 5 solid rounds, but those 2nd and 3rd attacks may miss and he has few effective defenses (no expertise, no close quarters combat, no combat reflexes, no improved initiative) if he finds himself disadvantaged. He's also given up on his mount or a cohort. It would be an interesting often powerful character, but it wouldn't break my game any. What's he going to do if the final monster proves to be 30HD grey render?
Why does 'Extra Rage' give two extra rages and 'Extra Smite' give only one smite? 'Rage' is a far more effective and general purpose damage dealer than 'Smite', plus aids the Barbarians critically weak Will saves. Perhaps because the designers knew that the Barbarian would seldom need extra rages, so what the heck.