Exactly. There was no need for this new internet censorship law at all, for they could've just started applying existing hate speech laws.
Instead they introduced this new shady law, which essentially turns social network companies into a part of the judicial branch.
The situation now is exactly as you have described it -- the companies fear the German fines and act overzealously.
Perhaps an outsourced, overzealous judicial branch is exactly what the German government wanted? As they're free of the restraints that bind the official judicial branch.