Unfortunately this isn't really a technical problem. Content ID exists to appease large organizations that sued YouTube into the ground for not doing enough to counter copyright infringement.

This claim process takes place before the legal copyright claim process. The legal process would require YouTube to take the video down immediately, and it would be required to stay down for at least two weeks even if the claim is bogus. (Or YouTube could decide not to follow the process and be held liable in case of actual infringement.)

There is no presumed innocence. The DMCA is constantly being abused, and the only possible punishment for malicious claims is an expensive lawsuit. It wouldn't surprise me at all if half of all DMCA takedown requests would be considered fair use in court, but the vast majority never get there.