You completely ignore that a full caster will have higher level spells with more effect for the same number of actions. 5th level throwing an 8d6 fireball and hitting several foes in a single action will probably do more damage than divine smite for the entire rest of the combat. Say it hits four and two save, that's 24d6 (avg 84 dmg). A paladin hits enough to use up his entire selection of spells (6 times), that's 14d8 (avg 54 dmg).
And the caster still has multiple actions more to add to it, even with cantrips. And for the next battle the caster still has spells but the paladin is completely out.
So no, that doesn't hold water when you actually try it out.