I can't tell you how many times I've seen YouTube videos taken down by "companies" with such names as "0wn3d Limited" and "Videosux Corp." The DMCA was broken from the start.
The whole point of that provision in the DMCA was that filing a lawsuit to get a judge to order something to be taken down takes time. If that takes two or three days to happen the damage can already be done by that point if the item in question is allowed to continue being hosted for all of that time.
The problem with the solution (DMCA) is that it also removes the monetary burden of filing a lawsuit (making it very low-risk to just file thousands of these things off per day, never intending to ever followup with a lawsuit) and the sanity filter (the judge).