I agree with removing DMCA protections for circumventing DRM instead of outlawing or creating legislative disincentives for DRM outright (that would be a can of worms). However, it still doesn't sound like a full solution. Registration of the sort you propose, if done correctly, could work for e-books or movies. But what does that kind of registration look like for server- or cloud-based content (e.g. MMOs, subscription-only software) or video games that constantly get constant updates and DLCs?
I can think of a number of possible solutions (update the DRM-free copy the LoC has as you push patches out, for example).
I think more interesting is the broader principle of withholding legal protection unless the company proactively provides a solution. Trying to mandate behavior by companies seems difficult to achieve politically, and leaves the government with the responsibility of enforcement. The enforcement/compliance work then scales based on the amount of creative material released with DRM. It seems unlikely that a government agency will keep up.
On the other hand, it costs the government nothing to withhold legal protection. Making it the company's responsibility to provide a DRM-free copy (or eventual activation keys, etc., details will vary) to a trusted government entity in order to opt-in to legal protection of their copyright scales 1-to-1. It also aligns the incentives of both sides of the copyright problem. Companies have the full protection of law during the period in which the copyright exists and the public benefits from works entering the public domain automatically. As an added bonus, the government has a central place to invest resources in archival and preservation of the huge swaths of our culture that we're currently in danger of losing. I'm very grateful for the Internet Archive but it is a shame that they have to operate based on volunteer donations. It would be great to have a means to take a means for the companies who created the content to fund is archival (via nominal fees for artifact registration).
The moment legal protection is withheld on disagreeable terms is the moment that copyrights become a less popular vehicle for defending a holder's rights. Despite what you might you might think, that's not a good thing. Copyrights are positive incentives for disclosure (but not necessarily for continued availability) of information. It is in the interest of a government for one to publicly disclose information on the sciences and the useful arts. Preemptively neutering a holder's defense to his copyright doesn't disincentives DRM. On the contrary, it encourages stronger, broader trade secret protections as well as non-disclosure and exclusion agreements with regards to both the content and DRM. That would be a blow to libraries just as much as it would archival sites.
