I think a situation where we're erring on the side of illegal content staying up until proven guilty is not the solution, although I don't disagree with your discomfort entirely - however I feel that the solution shouldn't be beholden to drawn out court battles one way or the other. 

Perhaps an ombudsman or an official framework for site owners to contest take-down notices, where both parties must present their reasoning, would be a better first step before approaching the courts.