Bishmon said:Wizard: Ouch, that archer up in the tree way over there is shooting at me with arrows! Hey, defender, a little help!
Paladin: Well, um, you see, I can't really invoke my remaining divine power to defend you, because in order to defend you, I have to attack something.
Wizard: What are you talking about? You have enough divine inspiration left that will allow you to defend me, but only while you're attacking something?
Paladin: My god works in mysterious ways.
Wizard: So, I'm guessing it's a no go with protection from that dragon that's flying towards us?
Paladin: You know the drill, not unless he gets within range of my sword.
Or maybe, the paladin can simply say: "Alright I'm going to use my smite, but I'm not going to attack anything, I'll use up a smite but can I just get the AC bonus?"
Dm: "Sure"
We don't know that you HAVE to attack a creature to gain the bonus, we just know that's part of the smite. Similar to how with defensive fighting you don't actually have to attack anything, you just have to give up your attack action.