Copyright law lacks the authority to deprive people of their constitutional rights.

Those rights would inevitably be violated as many bureaucratic functions of government require internet access, and not responding is not an option. It would also act to weaken the courts by setting the stage for further devolution of "rule of law" to "rule by law".

The simple claim and bureaucratic framework similar to DMCA would largely bypass the courts and deprive people of their paid services, as well as access needed for various societal tasks (i.e. passports, mail issues, taxes, etc) first without due process. Basically the same as getting an injunction without having to see a judge or provide adequate proof.

In other words the RIAA and their friends, under color of law may become its own kangaroo court or something along those lines.