This is subtle but it is hidden in the rules:
In order to play the card, you need to wear the Tower of Power Crown:
To play this card, wear the Tower of Power Crown. Then take the Stash Cards, and without looking, put them inside on top of your head.
But if you wear the crown, you need to wear the crown for the rest of the game:
You may never move Stash Cards from the Tower of Power Crown into your
own hand. It only protects you from stealing stealers who want to
steal cards from you. Continue wearing the Tower of Power for the
rest of the game.
So if you retrieve the card from the discard pile after it is played (and not noped) then you can't play it anymore because you can't wear the crown.
You could play it if you already have the crown, but it does nothing because the stash is also empty.
So there is no way you can gain any benefit from playing the card a second time in the same game. So you better use your five of a kind to find a useful card.
By the way, the crown is awesome: