Just extending your thought farther, why have police then as well? Shouldn't an individual protect themselves? If I am stronger then you and you can't protect your rights does that mean I am now right by taking them away for myself? If everyone was required to protect their own rights things would get messy fast.
I do look forward to the day, and I believe it will come, where companies and individuals will be handsomely fined for any false copyright claims.
There is no copyright police. People do defend themselves - they pay the police to do so and so do businesses. EU is not instituting a copyright police- it is asking internet media to set it up and pay for it.
Copyright owners have successfully lobbied with the argument: "It is soooo much effort to go after each case, and these platforms make it so easy to infringe they are essentially complicit".