Reason to: Collect Those Caps
Because you somehow can shapeshift into the last person that worn them complete with all their memories and everything you need to pass as them, as long as you put on those caps and it stayed on your head.
Taking it off returned you to your normal form and it only worked once, because after that, since you're the last person wearing those caps, you will not transform into anyone else. Unless, you return those caps to its rightful owner and the owner wears it once more before you take the cap again. Another way is to let someone else you targeted wear that used cap and you then can shift into their exact copy so yes, the cap doesn't have to go back to its original owner for it to work again.
All in all, quite a useful power. It helps well if you planned on to do some nifty little trick for some quick fun of shenanigan, but definitely not a long-lasting solution if you want to move on with an entirely brand new life and body