The DMCA requires carriers like Youtube to:
>[A service provider shall not be liable if] (E) if the person described in paragraph (1)(A) makes that material available online without the authorization of the copyright owner of the material, the service provider responds expeditiously to remove, or disable access to, the material
https://www.law.cornell.edu/uscode/text/17/512
The Youtube Copyright Strikes system being employed here (which is NOT the ContentID system) IS the DMCA Safe-Harbor compliant take-down system which was designed, developed and used exclusively because of the DMCA law!
The DMCA law does not provide for a government based form or system for takedowns, rather, it places the onus of a takedown system on the safe harbor who wishes to be safe.
This is DMCA request! You just apparently do not realize that the DMCA makes providers like Youtube create their own in-house DMCA take-down mechanisms.