Unless they're legally obligated to show proof of copyright registration for the takedown notice to be a valid, it would be risky to assume they didn't register it just because they didn't show proof.
This suggests an online process which looks like this:
* US Service provider offers web page for DMCA notices.
* Web page requests that the user enter copyright registration info.
* If user fails to provide registration info, web page offers links to various national copyright registration sites to register a copyright. A payment receipt for copyright registration is acceptable as temporary proof of registration, but must be followed up within some period of time by actual proof of registration.
* Temporary proof of registration is enough for a takedown, but the material will go back up if full proof is not submitted later.
This would put a big dent in nuisance DMCA claims. The service provider might get sued occasionally, but for big providers, it's probably worth litigating this once or twice. The companies that have valuable IP file copyright registrations. Disney will be able to show a copyright registration on all their movies.