The DMCA completely ignores how the digital world works; it was written in an age where interacting with the American legal system required you to have somebody physically located in the US.
Back then, you didn't need any technical safeguards against this kind of abuse. As long as such abuse was illegal, and there was police to arrest those committing the crimes, it was enough. In technical terms, the security was implemented on a completely different layer of the stack.
This is no longer the world we live in. There's nothing stopping somebody from e.g. Russia from pretending they're a relevant copyright agent, and forcing Youtube to remove anti-Putin videos.