The DMCA works very well for copyright owners, our users, and us as a web host. Here's how the process should work for an abusive DMCA request:
1- DMCA request (seemingly legitimate) is received, including a statement under penalty of perjury that the sender is the copyright owner.
2- Host contacts the site owner/removes the content.
3- Site owner is the legitimate owner of the content, so files a DMCA counter-notification with the host, with a statement under penalty of perjury that they are the copyright owner.
4- Host immediately brings disputed content back online. One of the parties is guilty of perjury, and they are both free to duke it out in court to have the content removed. Content can and will remain online until a court orders it removed. Web host has no liability for content remaining online (even if the counter-notification was bullshit), and the matter is presented and judged where it should be for such a dispute: in court.
If you believe that someone filed a bogus DMCA notice against your content, immediately file a counter-notice and your content should be immediately (or shortly, if not automated) back online. Then, you can sue the person who filed the complaint, and they will have quite a bit of responsibility and liability.
Sounds like the real fault in the process is that no-one understands it and that the system doesn't make itself accessible to the average lay-person. Maybe what we really need is a site that explains everything more clearly and makes filing a notice/counter-notice much simpler.