I believe the text of the DMCA is written to cause this. If you are an ISP, and you don't want to be liable for infringments, you have to take things down after receiving a DMCA takedown notice. The end.
You can put it back up after the user has followed the right procedure to challenge and assume liability themselves. I admit I'm not sure exactly what procedure the DMCA outlines for this.
I think what ISP's _could_ do is facilitate user's filing challenges more easily. But they've got to take it down after receiving a takedown request, that's pretty much what the law says (or else the ISP can be sued for the copyright infringement too).
Theoretically you can sue someone for issuing a takedown request in bad faith. Perhaps ISP's could help their users do this too, but it could get sticky for them.