This kind of effect is miserable to play with in a vacuum since you'll see crud that you'd rather tuck, bury or exile over and over.

Symmetry doesn't do this design any favor. At rare I want the version that only benefits myself.

Being such a minor durcly effect this probably would be better on a creature body.

One way this design might become infinitely more interesting: Add an activated ability to sacrifice this (and probsbly pay a mana cost) to reveal/exile the top three cards of your library and do something if you assemble a certain combination of cards e. g. you may play a card that shares a name with another card revealed/exiled this way and put the other ones sharing its name into your hand. That way the pushing back becomes inherently meaningful.