What you've described is largely how the DMCA already works.
1. Copyright holder files a claim.
2. Platform takes down content, and notifies the poster of the content.
3. If poster thinks the claim is incorrect, poster notifies the platform.
4. Platform restores the content, and notifies the copyright owner.
5. If the copyright owner wants the content taken down again, they have to sue the poster.
If the copyright owner must swear that they believe their claim is true. If they intentionally make a false claim it is perjury.
All that's really missing is it sounds like you would penalize the copyright owner for being wrong about fair use regardless of whether they were wrong because they honestly thought it was not fair use or they were wrong because they knew it was fair use but lied about it.
Fair use is subjective and tricky enough that it is not at all uncommon for both side to go into a case expecting for the court to go their way.
Some major platforms don't follow the above, because they have decided to handle copyright using their own procedures instead of following the DMCA procedures.
I know how the DMCA works. The problem is step 2. Step two should be "platform notifies possible violator that claim has been made". The platform should not be punished for leaving the content up. Right now, under the DMCA, if they leave the content up, they become liable. That should not be the case.
Furthermore, YouTube et al don't follow the DMCA. Their process is outside the DMCA, and starts with automated enforcement on behalf of the copyright holder, with no recourse for the potential violator.
1. Copyright holder files a claim.
2. Platform takes down content, and notifies the poster of the content.
3. If poster thinks the claim is incorrect, poster notifies the platform.
4. Platform restores the content, and notifies the copyright owner.
5. If the copyright owner wants the content taken down again, they have to sue the poster.
If the copyright owner must swear that they believe their claim is true. If they intentionally make a false claim it is perjury.
All that's really missing is it sounds like you would penalize the copyright owner for being wrong about fair use regardless of whether they were wrong because they honestly thought it was not fair use or they were wrong because they knew it was fair use but lied about it.
Fair use is subjective and tricky enough that it is not at all uncommon for both side to go into a case expecting for the court to go their way.
Some major platforms don't follow the above, because they have decided to handle copyright using their own procedures instead of following the DMCA procedures.