Asking search engines not to display stuff that is out there is certainly problematic. No doubt about that. However, they are already required to filter out links to copyrighted material, so the principle of filtering out certain things for legal reasons is already established.
It seems disproportionate to protect copyright holders from economic damage but refuse to protect individuals against being stigmatized forever because of some mistake they made many years ago based on a principle that has already been breached.
Adequately? Try suing some anonymous person X who posted something on a site S hosted in country C, describing something you allegedly did in country D, while you live in country E. Then try removing that data from site T in country F quoting the now removed data from site S.
It seems disproportionate to protect copyright holders from economic damage but refuse to protect individuals against being stigmatized forever because of some mistake they made many years ago based on a principle that has already been breached.