"Exactly as horrible" is unfair to you. But it sounds like you're advocating to give up on rule of law and just have the strongest most violent people be the ones to decide what's right. And I'd argue that you'd just get back to where we are right now: wealthy people would control the system, they'd employ strong violent people to enforce their personal whims as "law", and you'd be complaining that nobody is willing to beat up the pedophile (because his friends would hire goons to kill them).

I mean, presumably that's what's stopping you personally from implementing your own recommendation, right? Because if you showed up and kicked this guy's ass you'd be beaten and arrested by the police.