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".
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.