That's not the point and no, no champion can really do what Shaco does effectively. What Shaco does is play with the enemy team. Constantly BMing and taunting them to come get him, not because he can kill them, but because they can't catch him. Shaco becomes this looming threat that you never know where he is and even if you manage to chase him off of an objective, he'll pop up right back where he was, doing the same exact thing, forcing more and more of your team to respond to him.
Shaco does what he does because Shaco just doesn't die. Without point and click CC, Shaco becomes incredibly infuriating to play against with his Deceive jukes, boxes all in your jungle, and burst damage on your carries whenever he decides to show up out of nowhere.
Shaco's pushing bot lane and you send someone to run him off. If you shove it and leave, Shaco has
, so he'll be shoving it right back all over again. If you stick around to push the lane yourself, you're open to getting ganked by Shaco or worse yet, Shaco just wandered back over to his team and has engaged by picked someone out and then wandering toward top lane to start pushing that one in. All the while you're stuck diddling around bot lane, trying to make sure that your towers aren't being taken for free.