And you missed the point that if the pally wants to put it on someone, that person will likely already have to be in a position where he won't need to smite after, because the person is already helpless...
Depends on the campaign, actually. If the paladin is
investigating things, as I said, then he would
ask the person to put it on. You know, so he could figure out if combat was necessary.
And yes, I listed off a very small portion of things that Detect Evil doesn't work against.
By default, if the combat has already started, or if Detect Evil already "pops" against the person, the pally couldn't care less about the ring. But if he is investigating things that you've done, but you're there maintaining a deception of helping him, while you actually steer him toward your rivals, then it does help. Because your evil rivals won't know what you're up to. So pally puts ring on them, it reveals that they're not good, pally fights other evils, you mop up.